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# 11 finance problems: yield to maturity, price of stock, ROR, Beta, price of bond

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I have attached some sample problems for a test review. I would like to know the answer and how to work these problems. These questions are from a managerial finance class.

Finance Problems:

1. Bond's par value- \$1,000 pays coupons Semi-annually and matures in 16 years. Coupon Rate is 8% Coupons are paid semi annually. Price of Bond= \$666.65. What is yield to maturity of bonds?

A. 6.5%
B. 14.5%
C. 13%
D. 8%

2. Common stock pays dividends at the end of 5 years of \$4.10 expected to grow at rate of 2.8% forever. Required rate of return is 15.7%. At what price can stock be sold immediately after receiving the dividend?

A. \$32.67
B. 37.51
C. 29.39
D. 26.11

3. Standard deviation of probability distribution?

Return -17% 19% 25%
Probability .35 0.5 0.15

a. 16.07%
b. 17.95%
c. 17.05%
d. 18.04%

4. Required rate of return for a common stock using capital asset pricing is 17.8%, risk free rate of 7.12, rate of return 12.5%. What is beta?

a. 1.49
b. 1.42
c. 1.00
d. 1.99

5. Investment bought for \$1,000 and sold year later for \$1150 after receiving dividends of \$120 at end of year. What is the rate of return earned?

a. 11.00%
b. 15.00%
c. 3.00%
d. 27.00%

6. Common stock to pay dividends of \$3.20, \$5.30, \$4.00, \$4.10 at end of next four years respectively. Dividends grow at rate of 3.5% forever. Required rate of return is 14.2%. What is the price of stock?

a. \$39.66
b. 35.28
c. 38.99
d. 43.90

7. Bonds Par Value of \$3000 matures in 12 years. Coupon rate is 11%. Required rate of return is 9.83%. What is the price of Bond?

a. \$3,326.54
b. \$3,251.54
c. \$2,772.12
d. \$3,241.17

8. Firm to purchase free cash flows at \$3.20, \$5.30 and \$4.10 million at end of next 3 years. Grow 2.4% cash flow forever. Weighted average cost of capital is 16.2% value.

a. 0.07
b. 28.68
c. 30.42
d. 34.62

9. Firm purchased an asset two years ago for \$118,000 and spent another \$34,000 installation expenses. Asset falls within the five year macrs class for depreciation purposes. Tax rate 40%. What is the amount of taxes paid if asset is sold for \$63,000?

10. Firm estimating terminal cash flows for project involving acquisition of machine. Machine sold \$31,000 at end of life 3 years from today. Additional working capital of \$24,000 required. Machine purchased \$158,000 and \$18,000 install expense. What is terminal cash inflow for project if tax rate is 40% and machine in 5 year macrs?

11. Beta can be negative
True or False?

#### Solution Preview

The solutions are as follows:

1. The formula for calculating Present Value (PV) of a bond is:
PV = C/YTM[1 - 1/(1+YTM/2)^2n] + F/(1+YTM/2)^2n

where, C=Coupon=\$80, n=number of years to maturity and F=face value=\$1000.

Now it's very difficult to calculate the YTM without using a spreadsheet. Another method is, since we have the alternatives we will do reverse engineering.

Keep one important thing in mind, when the bond is selling below par it means YTM>C therefore, our answer can be only 13% or 14.5%.

Let's put 13% as YTM in the above equation, we get:
PV = 80/0.13[1 - 1/(1.065)^32] + 1000/(1.065)^32 = \$666.65, hence the answer is 13%.

...

#### Solution Summary

The solution calculates each problem showing all the formulas including discussion about the problems. The answers are given. No Excel formatted in this problem.

\$2.49