# Finance Calculations

Calculation:
1. A 3-year U.S. Treasury bond with a face value of \$1,000 pays a coupon of 6.25%. Coupon
is to be paid semi-annually. The reported annual yield to maturity is 6.8%. Solve the
following questions:
a. What is the present value of the bond?
b. What is the duration of the bond?
c. If the yield to maturity changes to 2%, what will be the present value?
d. If the yield to maturity changes to 7%, what will be the present value?
e. If the yield to maturity changes to 16%, what will be the present value?
2. The 7.9%, 5-year bond yields 5.9%. If this yield to maturity remains unchanged, what
will be its price one year after? Assume annual coupon payments and a face value of
\$1,000. What is the total return to an investor who held the bond over this year?
3. A government bond matures in 4 years, makes annual coupon payments of 5.8% and
offers a yield of 3.8% annually compounded. Assume face value is \$1,000.
a. Suppose that one year later the bond still yields 3.8%. What return has the bondholder
earned over the 12-month period?
b. Now suppose that the bond yields 2.9% at the end of the year. What return did the
bondholder earn in this case?
4. Assume coupons are paid annually. Here are the prices of three bonds with 10-year
maturities. Assume face value is \$100.
Bond coupon (%) Price (%)
3 87.00
5 106.00
9 137.00
a. What is the yield to maturity of each bond?
b. What is the duration of each bond?
5. A bond’s credit rating provides a guide to its price. Assume Aaa bonds yield 3.8% and
Baa bonds yield 4.7%. Assume a 10% six-year bond with annual coupons and a face
value of \$1,000.
a. What is the bond’s price if it is rated as Aaa?
b. What is the bond’s price if it is rated as Baa?
6. Company Z’s earnings and dividends per share are expected to grow indefinitely by 3%
a year. If next year’s dividend is \$9 and the cost of capital is 13%, what is the current
stock price?
7. Pharmecology just paid an annual dividend of \$1.90 per share. It’s a mature company,
but future EPS and dividends are expected to grow with inflation, which is forecasted
at 4.70% per year. The nominal cost of capital is 11.35%.
a. What is Pharmecology’s current stock price?
b. What would be Pharmecology’s current stock price using forecasted real dividends
and a real discount rate?
8. Consider the following three stocks:
▪ Stock A is expected to provide a dividend of \$12.10 a share forever.
▪ Stock B is expected to pay a dividend of \$6.10 next year. Thereafter, dividend growth
is expected to be 5.00% a year forever.
▪ Stock C is expected to pay a dividend of \$4.90 next year. Thereafter, dividend growth
is expected to be 21.00% a year for five years (i.e., years 2 through 6) and zero
thereafter.
If the required rate of return for each stock is 12.00%, what is the stock price for each of
the stocks?
9. Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has
grown rapidly. Forecasts made in 2019 are as follows:
(\$ millions) 2020 2021 2022 2023 2024
Net income 1.0 2.5 4.2 4.7 5.0
Investment 1.0 1.5 1.7 1.9 1.9
Free cash flow 1.0 1.0 2.5 2.8 3.1
Phoenix’s recovery will be complete by 2024, and there will be no further growth in net
income or free cash flow.
a. Calculate the PV of free cash flow, assuming a cost of equity of 10%.
b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?
10. The forecasted earnings and dividends for Growth-Tech are as follows:
Year 1 2 3 4
Book equity 10.00 12.00 14.40 15.55
Earnings per share (EPS) 2.50 3.00 2.30 2.48
Return on equity (ROE) 0.25 0.25 0.16 0.16
Payout ratio 0.20 0.20 0.50 0.50
Dividends per share (DIV) 0.50 0.60 1.15 1.24
Growth rate of dividends (%) — 20 92 8
The opportunity cost of capital is r = 0.12. The growth rate in year 4 remains constant
thereafter.
a. Calculate the value of Growth-Tech stock.
b. What part of the stock value reflects the discounted value of P3, the price forecasted
for year 3?
c. What part of P3 reflects the present value of growth opportunities (PVGO) after year
3?
11. Find Walmart’s consolidated balance sheets and income statements for fiscal year 2017
from SEC edgar. At the end of fiscal 2017, Walmart had 2,960 million shares outstanding
with a share price of \$106. The company’s weighted-average cost of capital was about
5%. Assume the marginal corporate tax rate was 35%. Calculate:
a. Market value added and Market-to-book ratio
b. Economic value added, ROC, ROA, and ROE
c. NWC in 2016 and 2017

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