What is the expected real interest rate the one-year spot


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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.)

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

      ($ 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

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