Dividends and Other Payouts. Issuing Equity Securities to the Public. Long-Term Debt. Options and Corporate Finance: Basic Concepts. Options and Corporate Finance: Extensions and Applications. Warrants and Convertibles. Derivatives and Hedging Risk. Short-Term Finance and Planning.
Cash Management. Credit Management. Mergers and Acquisitions. Financial Distress. International Corporate Finance.
Save my name, email, and website in this browser for the next time I comment. Ross, W. The Time Value of Money 6. Long-Term Financing: An Introduction Capital Structure: Basic Concepts Explanation: Given information: A portfolio has three stocks. Explanation: The cost of capital associated with an investment depends on the investment risk that Explanation: Given information: The debt-equity ratio of Company C is 1. Explanation: The various considerations in selecting the venture capitalist that are significant are Explanation: Companies use cash for the day-to-day operations of the business.
Accounts payable Explanation: If a firm has too much cash than it requires for the operations and planned expenses, Explanation: The cross rate is the implicit rate of exchange between two currencies mainly, they More Editions of This Book Corresponding editions of this textbook are also available below:.
F Essn. Essentials of Corporate Finance. Essentials of Corporate Finance with Connect Plus. Essentials of Corp. Finance - With Connect. Loose Leaf for Essentials of Corporate Finance. Essentials of Corporate Finance with Connect. The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows.
Here the cash flows are annual and the given interest rate is annual, so we can use the interest rate given. We simply find the PV of each cash flow and add them together. The total interest paid by First Simple Bank is the interest rate per period times the number of periods. In other words, the interest by First Simple Bank paid over 10 years will be:. Here we need to convert an EAR into interest rates for different compounding periods. Here we need to find the FV of a lump sum, with a changing interest rate.
We must do this problem in two parts. We need to find the annuity payment in retirement. Our retirement savings ends and the retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings.
We need to find the FV of a lump sum in one year and two years. It is important that we use the number of months in compounding since interest is compounded monthly in this case. We could find the EAR, and use the number of years as our compounding periods. We have simply made sure that the interest compounding period is the same as the number of periods we use to calculate the FV. Here we are finding the annuity payment necessary to achieve the same FV. The interest rate given is a 10 percent APR, with monthly deposits.
We must make sure to use the number of months in the equation. In this example, by reducing the savings period by one-half, the deposit necessary to achieve the same terminal value is about nine times as large. The number of periods is four, the number of quarters per year. Since we have an APR compounded monthly and an annual payment, we must first convert the interest rate to an EAR so that the compounding period is the same as the cash flows.
We can use the present value of a growing perpetuity equation to find the value of your deposits today. Here we are given the FVA, the interest rate, and the amount of the annuity.
We need to solve for the number of payments. Here we are given the PVA, number of periods, and the amount of the annuity. We need to solve for the interest rate. If you use trial and error, remember that increasing the interest rate lowers the PVA, and increasing the interest rate decreases the PVA. The amount of principal paid on the loan is the PV of the monthly payments you make. We are given the total PV of all four cash flows.
If we find the PV of the three cash flows we know, and subtract them from the total PV, the amount left over must be the PV of the missing cash flow. To solve this problem, we simply need to find the PV of each lump sum and add them together. Here we are finding interest rate for an annuity cash flow. We are given the PVA, number of periods, and the amount of the annuity. We should also note that the PV of the annuity is not the amount borrowed since we are making a down payment on the warehouse.
To find the interest rate, we need to solve this equation on a financial calculator, using a spreadsheet, or by trial and error. The profit the firm earns is just the PV of the sales price minus the cost to produce the asset. We want to find the value of the cash flows today, so we will find the PV of the annuity, and then bring the lump sum PV back to today. To find the value today, we find the PV of this lump sum.
This question is asking for the present value of an annuity, but the interest rate changes during the life of the annuity. We need to find the present value of the cash flows for the last eight years first. Now we can discount this lump sum to today. Here we are trying to find the dollar amount invested today that will equal the FVA with a known interest rate, and payments.
First we need to determine how much we would have in the annuity account. In other words, the interest rate quoted in the problem is only relevant to determine the total interest under the terms given. The cash flows in this problem are semiannual, so we need the effective semiannual rate. So, the value at the various times the questions asked for uses this value 9 years from now. To do this, you need the EAR. To calculate the PVA due, we calculate the PV of an ordinary annuity for t — 1 payments, and add the payment that occurs today.
We then use this value as the PV of an ordinary annuity. The payment for a loan repaid with equal payments is the annuity payment with the loan value as the PV of the annuity.
The ending balance is the beginning balance minus the principal payment. The ending balance for a period is the beginning balance for the next period. The interest payment is the beginning balance times the interest rate for the period, and the total payment is the principal payment plus the interest payment. This is because more principal is repaid early in the loan, which reduces the total interest expense over the life of the loan. Challenge The cash flows for this problem occur monthly, and the interest rate given is the EAR.
Since the cash flows occur monthly, we must get the effective monthly rate. One way to do this is to find the APR based on monthly compounding, and then divide by The amount needed at retirement is the PV of the monthly spending plus the PV of the inheritance.
To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The interest rate we would use for the leasing option is the same as the interest rate of the loan. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same.
To find the quarterly salary for the player, we first need to find the PV of the current contract. The cash flows for the contract are annual, and we are given a daily interest rate. We need to find the EAR so the interest compounding is the same as the timing of the cash flows. We can simply subtract this amount from the PV of the new contract. The remaining amount will be the PV of the future quarterly paychecks.
Using the daily interest rate, we can find the quarterly interest rate using the EAR equation, with the number of days being Here we have cash flows that would have occurred in the past and cash flows that would occur in the future.
We need to bring both cash flows to today. Before we calculate the value of the cash flows today, we must adjust the interest rate so we have the effective monthly interest rate. Finding the APR with monthly compounding and dividing by 12 will give us the effective monthly rate. Alternatively, we could have found the FV of the lump sum with the effective monthly rate as long as we used 12 periods.
The answer would be the same either way. In this problem, we are calculating both the PV and FV of annuities. So, by a lower interest rate, we are lowering the value of the back pay. But, we are also increasing the PV of the future salary. Since the future salary is larger and has a longer time, this is the more important cash flow to the plaintiff.
Again, to find the interest rate of a loan, we need to look at the cash flows of the loan. This is the same question as before, with different values.
Remember, we need to use the actual cash flows of the loan to find the interest rate. Be careful of interest rate quotations. The actual interest rate of a loan is determined by the cash flows. Here we are solving a two-step time value of money problem. Each question asks for a different possible cash flow to fund the same retirement plan.
Each savings possibility has the same FV, that is, the PV of the retirement spending when your friend is ready to retire. If your friend makes equal annual deposits into the account, this is an annuity with the FVA equal to the amount needed in retirement. Here we need to find a lump sum savings amount. In this problem, we have a lump sum savings in addition to an annual deposit.
Since we already know the value needed at retirement, we can subtract the value of the lump sum savings at retirement to find out how much your friend is short. We will calculate the number of periods necessary to repay the balance with no fee first. We simply need to use the PVA equation and solve for the number of payments. We need to find the FV of the premiums to compare with the cash payment promised at age We have to find the value of the premiums at year 6 first since the interest rate changes at that time.
Note, we could also compare the PV of the two cash flows. Whenever you are comparing two or more cash flow streams, the cash flow with the highest value at one time will have the highest value at any other time.
How much will it be worth? The monthly payments with a balloon payment loan are calculated assuming a longer amortization schedule, in this case, 30 years. We can solve using trial and error, a root-solving calculator routine, or a spreadsheet. Here we need to find the interest rate that makes us indifferent between an annuity and a perpetuity. To solve this problem, we need to find the PV of the two options and set them equal to each other.
The cash flows in this problem occur every two years, so we need to find the effective two year rate. One way to find the effective two year rate is to use an equation similar to the EAR, except use the number of days in two years as the exponent. We use the number of days in two years since it is daily compounding; if monthly compounding was assumed, we would use the number of months in two years.
In this problem, since the cash flows are two years apart, we have found the value of the perpetuity one period two years before the first payment, which is one year ago. We need to compound this value for one year to find the value today. In this case, when we use the PV of a perpetuity equation, we find the value of the perpetuity two years from today. We need to find the first payment into the retirement account.
Since the savings are in the form of a growing annuity, we can use the growing annuity equation and solve for the payment.
Since your salary is increasing at 3 percent, and the savings are increasing at 3 percent, the percentage of salary will remain constant. In a discount loan, the amount you receive is lowered by the discount, and you repay the full principal. To answer this, we need to diagram the perpetuity cash flows, which are: Note, the subscripts are only to differentiate when the cash flows begin. The cash flows are all the same amount.
We are only concerned with the time it takes money to double, so the dollar amounts are irrelevant. Enter 15 8. Enter 8 8. Enter 20 Enter 10 6. Enter Enter 60 7.
Enter 0. Enter 1, Enter 6 2. Enter 12 1. Enter 8 9. You would be indifferent when the PV of the two cash flows are equal. Enter 5. Solve for the payment under these circumstances.
Without fee: Enter As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury securities have substantial interest rate risk. All else the same, the Treasury security will have lower coupons because of its lower default risk, so it will have greater interest rate risk. If the bid price were higher than the ask price, the implication would be that a dealer was willing to sell a bond and immediately buy it back at a higher price.
How many such transactions would you like to do? Prices and yields move in opposite directions. Since the bid price must be lower, the bid yield must be higher. There are two benefits. First, the company can take advantage of interest rate declines by calling in an issue and replacing it with a lower coupon issue. Second, a company might wish to eliminate a covenant for some reason. Calling the issue does this.
The cost to the company is a higher coupon. The cost to the company is that it may have to buy back the bond at an unattractive price.
Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used to establish the coupon rate necessary for a particular issue to initially sell for par value.
Bond issuers also simply ask potential purchasers what coupon rate would be necessary to attract them. The required return is what investors actually demand on the issue, and it will fluctuate through time.
The coupon rate and required return are equal only if the bond sells for exactly at par. Some investors have obligations that are denominated in dollars; i. Their primary concern is that an investment provide the needed nominal dollar amounts.
Pension funds, for example, often must plan for pension payments many years in the future. If those payments are fixed in dollar terms, then it is the nominal return on an investment that is important.
Companies pay to have their bonds rated simply because unrated bonds can be difficult to sell; many large investors are prohibited from investing in unrated issues. Treasury bonds have no credit risk since it is backed by the U. The term structure is based on pure discount bonds. The yield curve is based on coupon-bearing issues. Bond ratings have a subjective factor to them.
Split ratings reflect a difference of opinion among credit agencies. As a general constitutional principle, the federal government cannot tax the states without their consent if doing so would interfere with state government functions. At one time, this principle was thought to provide for the tax-exempt status of municipal interest payments.
However, modern court rulings make it clear that Congress can revoke the municipal exemption, so the only basis now appears to be historical precedent. One measure of liquidity is the bid-ask spread. Liquid instruments have relatively small spreads. Looking at Figure 7. Generally, liquidity declines after a bond is issued. Some older bonds, including some of the callable issues, have spreads as wide as six ticks. Companies charge that bond rating agencies are pressuring them to pay for bond ratings.
When a company pays for a rating, it has the opportunity to make its case for a particular rating. With an unsolicited rating, the company has no input. A year bond looks like a share of preferred stock. In particular, it is a loan with a life that almost certainly exceeds the life of the lender, assuming that the lender is an individual.
With a junk bond, the credit risk can be so high that the borrower is almost certain to default, meaning that the creditors are very likely to end up as part owners of the business. The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms.
Unlike YTM and required return, the coupon rate is not a return used as the interest rate in bond cash flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount. For the example given, the coupon rate on the bond is still 10 percent, and the YTM is 8 percent. Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates rise—hence, the price of the bond decreases.
We will use this par value in all problems unless a different par value is explicitly stated. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. We will use this shorthand notation in remainder of the solutions key.
Here we need to find the YTM of a bond. First, we know the YTM has to be higher than the coupon rate since the bond is a discount bond. That still leaves a lot of interest rates to check. Here we need to find the coupon rate of the bond. To find the price of this bond, we need to realize that the maturity of the bond is 10 years. The bond was issued one year ago, with 11 years to maturity, so there are 10 years left on the bond.
Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. Here we are finding the YTM of a semiannual coupon bond. This is a bond since the maturity is greater than 10 years. The coupon rate, located in the first column of the quote is 6. Here we are finding the YTM of semiannual coupon bonds for various maturity lengths. Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately.
This is because we calculate the clean price of the bond. Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 8 percent. The company should set the coupon rate on its new bonds equal to the required return. The required return can be observed in the market by finding the YTM on outstanding bonds of the company. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment.
Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are five months until the next coupon payment, so one month has passed since the last coupon payment.
There are three months until the next coupon payment, so three months have passed since the last coupon payment. To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. Treasury bond with a similar maturity. The column lists the spread in basis points.
One basis point is one-hundredth of one percent, so basis points equals one percent. The spread for this bond is basis points, or 4. The bond price is the present value of the cash flows from a bond.
The YTM is the interest rate used in valuing the cash flows from a bond. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium, since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount since it provides insufficient coupon payments compared to that required by investors on other similar bonds.
For premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon rate. Current yield is defined as the annual coupon payment divided by the current bond price. For premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less than the YTM, and for bonds selling at par value, the current yield is equal to the YTM.
In all cases, the current yield plus the expected one-period capital gains yield of the bond must be equal to the required return. The price of a zero coupon bond is the PV of the par, so: a. Previous IRS regulations required a straight-line calculation of interest. The company will prefer straight-line methods when allowed because the valuable interest deductions occur earlier in the life of the bond. The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued.
The total coupon payment for the coupon bonds will be the number bonds times the coupon payment. For the cash flow of the coupon bonds, we need to account for the tax deductibility of the interest payments.
To do this, we will multiply the total coupon payment times one minus the tax rate. For the zero coupon bonds, the first year interest payment is the difference in the price of the zero at the end of the year and the beginning of the year. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year even though the company did not have a cash flow for the interest expense.
During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same.
This is because of the much larger repayment amount for the zeroes. We found the maturity of a bond in Problem However, in this case, the maturity is indeterminate. A bond selling at par can have any length of maturity. In other words, when we solve the bond pricing equation as we did in Problem 22, the number of periods can be any positive number. We first need to find the real interest rate on the savings. To find the capital gains yield and the current yield, we need to find the price of the bond.
The rate of return you expect to earn if you purchase a bond and hold it until maturity is the YTM. To find our HPY, we need to find the price of the bond in two years.
The price of any bond or financial instrument is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows.
To calculate this, we need to set up an equation with the callable bond equal to a weighted average of the noncallable bonds. We will invest X percent of our money in the first noncallable bond, which means our investment in Bond 3 the other noncallable bond will be 1 — X. This combination of bonds should have the same value as the callable bond, excluding the value of the call.
In general, this is not likely to happen, although it can and did. The reason this bond has a negative YTM is that it is a callable U. Treasury bond. Market participants know this. Given the high coupon rate of the bond, it is extremely likely to be called, which means the bondholder will not receive all the cash flows promised. A better measure of the return on a callable bond is the yield to call YTC. The YTC calculation is the basically the same as the YTM calculation, but the number of periods is the number of periods until the call date.
If the YTC were calculated on this bond, it would be positive. To find the present value, we need to find the real weekly interest rate. To find the real return, we need to use the effective annual rates in the Fisher equation. The real cash flows are an ordinary annuity, discounted at the real interest rate. To answer this question, we need to find the monthly interest rate, which is the APR divided by We also must be careful to use the real interest rate.
The nominal monthly withdrawals will increase by the inflation rate each month. To find the nominal dollar amount of the last withdrawal, we can increase the real dollar withdrawal by the inflation rate. We can increase the real withdrawal by the effective annual inflation rate since we are only interested in the nominal amount of the last withdrawal.
Enter 16 7. Enter 20 4. Enter 29 3. If both bonds sell at par, the initial YTM on both bonds is the coupon rate, 8 percent. The company should set the coupon rate on its new bonds equal to the required return; the required return can be observed in the market by finding the YTM on outstanding bonds of the company.
The company will prefer straight-line method when allowed because the valuable interest deductions occur earlier in the life of the bond. Enter 8 5. The value of any investment depends on the present value of its cash flows; i.
The cash flows from a share of stock are the dividends. Investors believe the company will eventually start paying dividends or be sold to another company. In general, companies that need the cash will often forgo dividends since dividends are a cash expense.
Young, growing companies with profitable investment opportunities are one example; another example is a company in financial distress. This question is examined in depth in a later chapter. The general method for valuing a share of stock is to find the present value of all expected future dividends. The dividend growth model presented in the text is only valid i if dividends are expected to occur forever, that is, the stock provides dividends in perpetuity, and ii if a constant growth rate of dividends occurs forever.
A violation of the first assumption might be a company that is expected to cease operations and dissolve itself some finite number of years from now. The stock of such a company would be valued by applying the general method of valuation explained in this chapter.
This stock would also be valued by the general dividend valuation method explained in this chapter. The common stock probably has a higher price because the dividend can grow, whereas it is fixed on the preferred. However, the preferred is less risky because of the dividend and liquidation preference, so it is possible the preferred could be worth more, depending on the circumstances.
The two components are the dividend yield and the capital gains yield. For most companies, the capital gains yield is larger. This is easy to see for companies that pay no dividends. For companies that do pay dividends, the dividend yields are rarely over five percent and are often much less. If the dividend grows at a steady rate, so does the stock price.
In other words, the dividend growth rate and the capital gains yield are the same. In a corporate election, you can buy votes by buying shares , so money can be used to influence or even determine the outcome.
Many would argue the same is true in political elections, but, in principle at least, no one has more than one vote. Investors buy such stock because they want it, recognizing that the shares have no voting power. Presumably, investors pay a little less for such shares than they would otherwise. Presumably, the current stock value reflects the risk, timing and magnitude of all future cash flows, both short-term and long-term. If this assumption is violated, the two-stage dividend growth model is not valid.
In other words, the price calculated will not be correct. Depending on the stock, it may be more reasonable to assume that the dividends fall from the high growth rate to the low perpetual growth rate over a period of years, rather than in one year. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today.
We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. The required return of a stock is made up of two parts: The dividend yield and the capital gains yield.
The question asks for the dividend this year. The price of any financial instrument is the PV of the future cash flows.
The price a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. This stock has a constant growth rate of dividends, but the required return changes twice. To find the value of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever.
The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. We need to find the price here since the required return changes at that time. Here we have a stock that pays no dividends for 10 years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. We simply discount the future stock price at the required return.
The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends using the required return. With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period.
With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the futures stock price, plus the PV of all dividends during the supernormal growth period.
Here we need to find the dividend next year for a stock experiencing supernormal growth. We know the stock price, the dividend growth rates, and the required return, but not the dividend. Now we need to find the equation for the stock price today. The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth.
We are given the stock price, the dividend growth rate, and the required return, and are asked to find the dividend. The price of a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 10, so we can find the price of the stock in Year 9, one year before the first dividend payment. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield.
To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return required return minus the dividend yield. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time.
We can then use this interest rate to find the equivalent annual dividend. In other words, when we receive the quarterly dividend, we reinvest it at the required return on the stock.
So, the effective quarterly rate is: Effective quarterly rate: 1. This would assume the dividends increased each quarter, not each year. Here we have a stock with supernormal growth, but the dividend growth changes every year for the first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend.
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