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Chapter 4: 23BP (page 283)

Jack Hammer invests in a stock that will pay dividends of \(2.00 at the end of the first year; \)2.20 at the end of the second year; and \(2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for \)33. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.)

Short Answer

Expert verified

The present value is $29.47.

Step by step solution

01

Identification of the required information

Dividend at Year 1 (D1) = $2

Dividend at Year 2 (D2) = $2.2

Dividend at Year 3 (D3) = $2.4

Sale value at Year 3 (S) = $33

Interest Rate (i) = 11%

02

Present value (PV)

PV=D1脳1+i-n1+D2脳1+i-n2+D3脳1+i-n3+S脳1+i-n3=$2(1+11%)-1+$2.2脳(1+11%)-2+$2.4(1+11%)-3+$33脳(1+11%)-3=$29.47=$29.47

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Most popular questions from this chapter

Question:Surgical Supplies Corporation paid a dividend of $1.12 per share over the last 12 months. The dividend is expected to grow at a rate of 2.5 percent over the next three years (supernormal growth). It will then grow at a normal, constant rate of 7 percent for the foreseeable future. The required rate of return is 12 percent (this will also serve as the discount rate).

a. Compute the anticipated value of the dividends for the next three years (D1, D2, and D3).

b. Discount each of these dividends back to the present at a discount rate of 12 percent and then sum them.

c. Compute the price of the stock at the end of the third year (P3).

P3 = D4/ (Ke - g)

d. After you have computed P3, discount it back to the present at a discount rate of 12 percent for three years.

e. Add together the answers in part b and part d to get the current value of the stock. (This answer represents the present value of the first three periods of dividends plus the present value of the price of the stock after three periods.)

Tim Trepid is highly risk-averse while Mike Macho actually enjoys taking a risk.

a. Which one of the four investments should Tim choose? Compute coefficients of variation to help you in your choice.

Investments

Returns:

Expected Value

Standard Deviation

Buy stocks ..................................... \( 9,140 \) 6,140

Buy bonds ..................................... 7,680 2,560

Buy commodity futures ................. 19,100 26,700

Buy options ................................... 17,700 18,200

b. Which one of the four investments should Mike choose?

King鈥檚 Department Store is contemplating the purchase of a new machine for \(22,802. The machine will provide \)3,500 per year in cash flow for nine years. King鈥檚 has a cost of capital of 10 percent. Using the internal rate of return method, evaluate this project and indicate whether it should be undertaken.

Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point as described next:

Real rate of return ........................ 4%

Inflation premium ......................... 6

Risk premium .............................. 5

Total return ............................... 15%

Assume that five years later the inflation premium is only 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 20 years remaining until maturity. Compute the new price of the bond.

Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 9 percent annual interest. The current yield to maturity on such bonds in the market is 12 percent. Compute the price of the bonds for these maturity dates:

a. 30 years.

b. 15 years.

c. 1 year.
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