Calculate the PV of free cash flow, assuming a cost of equity of 10%.
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Problem 3-13 Term-structure theories
The one-year spot interest rate is r1 = 5.6%, and the two-year rate is r2 = 6.6%. If the expectations theory is correct, what is the expected one-year interest rate in one year’s time? (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
Real interest rate ≈ nominal interest rate − inflation rate
And
Nominal interest rate ≈ real interest rate + expected inflation rate
5.6+6.6=12.2
Expected interest rate | 12.2% |
Problem 3-14 Real interest rates
The two-year interest rate is 11.4%, and the expected annual inflation rate is 5.7%. | |
a. | What is the expected real interest rate? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Solution |
Real Interest Rate (R) = Nominal Interest Rate (r) – Rate of Inflation (i)
R= 11.4-5.7
=5.7%
Expected real interest rate | 5.7% |
It does not change in this case
Nominal rate | 11.4% |
Problem 4-6 Dividend discount model
Company Z-prime’s earnings and dividends per share are expected to grow by 5% a year. Its growth will stop after year 4. In year 5 and afterward, it will pay out all earnings as dividends. Assume next year’s dividend is $10, the market capitalization rate is 8% and next year’s EPS is $15. What is Z-prime’s stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
First we must determine the price based on dividends per share for years 1–4. Then, we must account for the growth in earnings per share. With next year’s EPS at $15 and EPS growing at 5% per year, the forecasted EPS at year 5 is $15 x (1.05)4 = $18.23. Therefore, the forecasted price per share at year 4 is $18.23/.08 = $227.91. Therefore, the current price is:
P0= 10/1.08+10.5/ (1.08)2+11.03/ (1.08)3+11.58/(1.08)4+227.91/(1.08)4
=203.05
Stock price | $203.05 |
Problem 4-28 Valuing free cash flow
Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made at the beginning of 2016 are as follows: | |||||
($ millions) | 2017 | 2018 | 2019 | 2020 | 2021 |
Net income | 1.0 | 3.3 | 5.8 | 6.3 | 6.6 |
Investment | 1.0 | 2.3 | 2.5 | 2.7 | 2.7 |
Free cash flow | 0 | 1.0 | 3.3 | 3.6 | 3.9 |
Phoenix’s recovery will be complete by 2021, and there will be no further growth in free cash flow. |
a. | Calculate the PV of free cash flow, assuming a cost of equity of 10%. (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) |
PV2016= DIV2017/ (1 + r) + DIV2018/ (1 + r)2+ DIV2019/ (1 + r)3+ DIV2020/ (1 + r)4+ DIV2021/ (1 + r)5+ (DIV2021/ r)/ (1 + r)5PV2016= $0 / 1.09 + $1 / 1.092+ $2 / 1.093+ $2.3 / 1.094+ $2.6 / 1.095 + ($2.6 / .09) / 1.095PV2016= $24.48 million
Present value | $24.8 million |
b. | Assume that Phoenix has 10 million shares outstanding. What is the price per share? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Price per share2016 = PV2016/ number of shares Price per share2016 = $24.48 / 12 Price per share2016 = $2.04 |
Price per share | $2.04 |
c. | What is Phoenix’s P/E ratio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Based on $1million of net income for 2016: P/E2016= $24.48 / $1 = 24.48 |
P/E ratio | 24.48 |