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# Present Value of a discount bond

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Find the present value (price) of a discount bond with a one-year term to maturity and a 10% yield. Next, find the price of a ten-year discount bond that also yields 10%. Now, increase the yield on both instruments to 11%. On a percentage basis, which instrument demonstrates the greatest change in price? What does this indicate about the price risk of the one-year bond in relation to an otherwise comparable 10-year bond, and what are the attendant implications?

#### Solution Preview

The following calculations have been with a HP 10BII financial calculator.

Q1. PV of a 1-year bond at 10%
N = 1 (years to maturity)
FV = \$1000 (face value of a bond is always \$1000)
I/Y = 10 % (yield to maturity)
PMT = 0
Solve for the present value PV = \$909.09

Q2. PV of a 10-year bond at 10%
N = 10 (years to maturity)
FV = \$1000 (face value)
I/Y = 10 % (yield to maturity)
PMT = 0
Solve for the present value PV = \$385.54

Q3. PV of a 1-year bond at 11%
N = 1 (years to maturity)
FV = \$1000 (face value)
I/Y = 11 % (yield to maturity)
PMT = 0
Solve for the present value PV = \$900.90

Q4. PV of a 10-year bond at 11%
N = 10 (years to maturity)
FV = \$1000 (face value)
I/Y = ...

#### Solution Summary

This solution compares 1-year and 10-year discount bonds when the yield to maturity increases from 10% from 11%, including a concise discussion of risk.

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## finance questions

Chapter 6
43.) Present and Future Values. The present value of the following cash flow stream is \$6,550 when discounted at 10 percent annually. What is the value of the missing cash flow?
Year Cash Flow
1 \$1,700
2 ?
3 \$2,100
4 \$2,800

Chapter 7
9.) Calculating Real Rates of Return. If treasury bills are currently paying 7 percent and the inflation rate is 3.8, what is the approximate real estate of interest? The exact real estate?

18.) Bond Yields. One More Time Software has 9.2 percent coupon bonds on the market with nine years to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. What is the current yield on the bonds? The YTM? The effective annual yield?

24.) Bond Prices versus Yields.
a.) What is the relationship between the price of a bond and it's YTM?
b.) Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at par value?
c.) What relationship between current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value?

Chapter 8
13.) Nonconstant Dividends. Far Side Corporation is expected to pay the following dividends over the next four years: \$11, \$8, \$5, \$2. Afterward, the company pledges to maintain a constant 5 percent growth rate in dividends forever. If the required return on the stock is 12 percent, what is the current share price?

14.) Supernormal Growth. Marcael Co. is growing quickly. Dividends are expected to grow at a 30 percent rate for the next three years, with the growth rate falling off to a constant 6 percent thereafter. If the required return is 13 percent and the company just paid a 1.80 dividend, what is the current share price?

22.) Capital Gains versus Income. Consider four different stocks, all of which have a required return of 19 percent and a most recent dividend of \$4.50 per share. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10 percent, 0 percent, and -5 percent per year, respectively. Stock Z is a growth stock that will increase its dividend by 20 percent for the next two years and then maintain a constant 12 percent growth rate thereafter. What is the dividend yield rate for each of these four stocks? What is the expected capital gains yield? Discuss the relationship among various returns that you find for each of these stocks.

Chapter 9
8.) Calculating NPV. For the following cash flows, suppose the firm uses the NPV decision rule. At a required return of 11 percent, should the firm accept this project? What is the required return was 30 percent?

13.) NPV versus IRR. Consider the following two mutually exclusive projects:
Year Cash Flow (X) Cash Flow (Y)
0 -\$15,000 -\$15,000
1 \$8,150 \$7,700
2 \$5,050 \$5,150
3 \$6,800 \$7,250
Sketch the NPV profiles for X and Y over a range of discount rates from zero to 25 percent. What is the crossover rate for these two projects?

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