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