# Calculate the PV of free cash flow, assuming a cost of equity of 10%.

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%

b-1. If the expected rate of inflation suddenly rises to 7.7%, what does Fisher’s theory say about how the real interest rate will change?

Rate Does not Change – This is the correct answer

 Real rate decreases
b-2. What about the nominal rate? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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