Valuing a business * Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2019 are as follows: 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 9%. b. Assume that Phoenix has 12 million shares outstanding. What is the price per share? c. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2020 to 2024.

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Answer 1

Textbook Question

Chapter 4, Problem 31PS

Valuing a business* Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2019 are as follows:

Chapter 4, Problem 31PS, Valuing a business Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow

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 9%.
b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?
c. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2020 to 2024.

a)

Expert Solution

Summary Introduction

To determine: Present value of free cash flow

Explanation of Solution

Compute the present value of free cash flow:

$PV2019= DIV20201+r+DIV2021(1+r)2+DIV2022(1+r)3+DIV2023(1+r)4+DIV2024(1+r)5+DIV2025r(1+r)5 =$01.09+$11.092+$21.093+$2.31.094+$2.61.095+ ($2.60.09)1.095=$24.48 million$

Hence, the present value is $24.8 million.

b)

Expert Solution

Summary Introduction

To determine: Price per share

Explanation of Solution

Note:

Assume no debt, the share price are as follows,

$Price per share2019 = PV2019Number of shares= $24.4812= $2.04$

Hence, the price per share is $2.04.

c)

Expert Solution

Summary Introduction

To confirm: The expected rate of return is 9%.

Explanation of Solution

Compute PV of the cash flows at various points in time:

$PV2020= $11.09+$21.092+ $2.31.093+$2.61.094+($2.60.09) 1.094= $26.68$

$PV2021= $21.09+$2.31.092+ $2.61.093+($2.6.09) 1.093= $28.09$

$PV2022= $2.31.09+$2.61.092+($2.6.09) 1.092= $28.61$

$PV2023= $2.6.09= $28.89$

$PV2024= $2.6.09= $28.89$

Compute rate of return using the formula $r0= (DIV1+P1–P0)P0$

$Rate of return2021= ($1+$28.09−$26.68)$26.68=0.09, or 9%$

$Rate of return2022= ($2+$28.61−$28.09)$28.09=0.09, or 9%$

$Rate of return2023= ($2.3+$28.89−$28.61)$28.61=0.09, or 9%$

$Rate of return2024= ($2.6+$28.89−$28.89)$28.89=0.09, or 9%$

Thus, the above calculation shows that the rate of return on Company P is exactly 9%.

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Answer 2

Textbook Question

Chapter 4, Problem 31PS

Valuing a business* Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2019 are as follows:

Chapter 4, Problem 31PS, Valuing a business Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow

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 9%.
b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?
c. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2020 to 2024.

a)

Expert Solution

Summary Introduction

To determine: Present value of free cash flow

Explanation of Solution

Compute the present value of free cash flow:

$PV2019= DIV20201+r+DIV2021(1+r)2+DIV2022(1+r)3+DIV2023(1+r)4+DIV2024(1+r)5+DIV2025r(1+r)5 =$01.09+$11.092+$21.093+$2.31.094+$2.61.095+ ($2.60.09)1.095=$24.48 million$

Hence, the present value is $24.8 million.

b)

Expert Solution

Summary Introduction

To determine: Price per share

Explanation of Solution

Note:

Assume no debt, the share price are as follows,

$Price per share2019 = PV2019Number of shares= $24.4812= $2.04$

Hence, the price per share is $2.04.

c)

Expert Solution

Summary Introduction

To confirm: The expected rate of return is 9%.

Explanation of Solution

Compute PV of the cash flows at various points in time:

$PV2020= $11.09+$21.092+ $2.31.093+$2.61.094+($2.60.09) 1.094= $26.68$

$PV2021= $21.09+$2.31.092+ $2.61.093+($2.6.09) 1.093= $28.09$

$PV2022= $2.31.09+$2.61.092+($2.6.09) 1.092= $28.61$

$PV2023= $2.6.09= $28.89$

$PV2024= $2.6.09= $28.89$

Compute rate of return using the formula $r0= (DIV1+P1–P0)P0$

$Rate of return2021= ($1+$28.09−$26.68)$26.68=0.09, or 9%$

$Rate of return2022= ($2+$28.61−$28.09)$28.09=0.09, or 9%$

$Rate of return2023= ($2.3+$28.89−$28.61)$28.61=0.09, or 9%$

$Rate of return2024= ($2.6+$28.89−$28.89)$28.89=0.09, or 9%$

Thus, the above calculation shows that the rate of return on Company P is exactly 9%.

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Answer 3

Textbook Question

Chapter 4, Problem 31PS

Valuing a business* Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2019 are as follows:

Chapter 4, Problem 31PS, Valuing a business Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow

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 9%.
b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?
c. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2020 to 2024.

a)

Expert Solution

Summary Introduction

To determine: Present value of free cash flow

Explanation of Solution

Compute the present value of free cash flow:

$PV2019= DIV20201+r+DIV2021(1+r)2+DIV2022(1+r)3+DIV2023(1+r)4+DIV2024(1+r)5+DIV2025r(1+r)5 =$01.09+$11.092+$21.093+$2.31.094+$2.61.095+ ($2.60.09)1.095=$24.48 million$

Hence, the present value is $24.8 million.

b)

Expert Solution

Summary Introduction

To determine: Price per share

Explanation of Solution

Note:

Assume no debt, the share price are as follows,

$Price per share2019 = PV2019Number of shares= $24.4812= $2.04$

Hence, the price per share is $2.04.

c)

Expert Solution

Summary Introduction

To confirm: The expected rate of return is 9%.

Explanation of Solution

Compute PV of the cash flows at various points in time:

$PV2020= $11.09+$21.092+ $2.31.093+$2.61.094+($2.60.09) 1.094= $26.68$

$PV2021= $21.09+$2.31.092+ $2.61.093+($2.6.09) 1.093= $28.09$

$PV2022= $2.31.09+$2.61.092+($2.6.09) 1.092= $28.61$

$PV2023= $2.6.09= $28.89$

$PV2024= $2.6.09= $28.89$

Compute rate of return using the formula $r0= (DIV1+P1–P0)P0$

$Rate of return2021= ($1+$28.09−$26.68)$26.68=0.09, or 9%$

$Rate of return2022= ($2+$28.61−$28.09)$28.09=0.09, or 9%$

$Rate of return2023= ($2.3+$28.89−$28.61)$28.61=0.09, or 9%$

$Rate of return2024= ($2.6+$28.89−$28.89)$28.89=0.09, or 9%$

Thus, the above calculation shows that the rate of return on Company P is exactly 9%.

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Answer 4

Textbook Question

Chapter 4, Problem 31PS

Valuing a business* Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2019 are as follows:

Chapter 4, Problem 31PS, Valuing a business Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow

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 9%.
b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?
c. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2020 to 2024.

a)

Expert Solution

Summary Introduction

To determine: Present value of free cash flow

Explanation of Solution

Compute the present value of free cash flow:

$PV2019= DIV20201+r+DIV2021(1+r)2+DIV2022(1+r)3+DIV2023(1+r)4+DIV2024(1+r)5+DIV2025r(1+r)5 =$01.09+$11.092+$21.093+$2.31.094+$2.61.095+ ($2.60.09)1.095=$24.48 million$

Hence, the present value is $24.8 million.

b)

Expert Solution

Summary Introduction

To determine: Price per share

Explanation of Solution

Note:

Assume no debt, the share price are as follows,

$Price per share2019 = PV2019Number of shares= $24.4812= $2.04$

Hence, the price per share is $2.04.

c)

Expert Solution

Summary Introduction

To confirm: The expected rate of return is 9%.

Explanation of Solution

Compute PV of the cash flows at various points in time:

$PV2020= $11.09+$21.092+ $2.31.093+$2.61.094+($2.60.09) 1.094= $26.68$

$PV2021= $21.09+$2.31.092+ $2.61.093+($2.6.09) 1.093= $28.09$

$PV2022= $2.31.09+$2.61.092+($2.6.09) 1.092= $28.61$

$PV2023= $2.6.09= $28.89$

$PV2024= $2.6.09= $28.89$

Compute rate of return using the formula $r0= (DIV1+P1–P0)P0$

$Rate of return2021= ($1+$28.09−$26.68)$26.68=0.09, or 9%$

$Rate of return2022= ($2+$28.61−$28.09)$28.09=0.09, or 9%$

$Rate of return2023= ($2.3+$28.89−$28.61)$28.61=0.09, or 9%$

$Rate of return2024= ($2.6+$28.89−$28.89)$28.89=0.09, or 9%$

Thus, the above calculation shows that the rate of return on Company P is exactly 9%.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a)

Expert Solution

Summary Introduction

To determine: Present value of free cash flow

Explanation of Solution

Compute the present value of free cash flow:

$PV2019= DIV20201+r+DIV2021(1+r)2+DIV2022(1+r)3+DIV2023(1+r)4+DIV2024(1+r)5+DIV2025r(1+r)5 =$01.09+$11.092+$21.093+$2.31.094+$2.61.095+ ($2.60.09)1.095=$24.48 million$

Hence, the present value is $24.8 million.

b)

Expert Solution

Summary Introduction

To determine: Price per share

Explanation of Solution

Note:

Assume no debt, the share price are as follows,

$Price per share2019 = PV2019Number of shares= $24.4812= $2.04$

Hence, the price per share is $2.04.

c)

Expert Solution

Summary Introduction

To confirm: The expected rate of return is 9%.

Explanation of Solution

Compute PV of the cash flows at various points in time:

$PV2020= $11.09+$21.092+ $2.31.093+$2.61.094+($2.60.09) 1.094= $26.68$

$PV2021= $21.09+$2.31.092+ $2.61.093+($2.6.09) 1.093= $28.09$

$PV2022= $2.31.09+$2.61.092+($2.6.09) 1.092= $28.61$

$PV2023= $2.6.09= $28.89$

$PV2024= $2.6.09= $28.89$

Compute rate of return using the formula $r0= (DIV1+P1–P0)P0$

$Rate of return2021= ($1+$28.09−$26.68)$26.68=0.09, or 9%$

$Rate of return2022= ($2+$28.61−$28.09)$28.09=0.09, or 9%$

$Rate of return2023= ($2.3+$28.89−$28.61)$28.61=0.09, or 9%$

$Rate of return2024= ($2.6+$28.89−$28.89)$28.89=0.09, or 9%$

Thus, the above calculation shows that the rate of return on Company P is exactly 9%.

Answer 8

a)

Expert Solution

Summary Introduction

To determine: Present value of free cash flow

Explanation of Solution

Compute the present value of free cash flow:

$PV2019= DIV20201+r+DIV2021(1+r)2+DIV2022(1+r)3+DIV2023(1+r)4+DIV2024(1+r)5+DIV2025r(1+r)5 =$01.09+$11.092+$21.093+$2.31.094+$2.61.095+ ($2.60.09)1.095=$24.48 million$

Hence, the present value is $24.8 million.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Summary Introduction

To determine: Present value of free cash flow

Answer 13

Explanation of Solution

Compute the present value of free cash flow:

$PV2019= DIV20201+r+DIV2021(1+r)2+DIV2022(1+r)3+DIV2023(1+r)4+DIV2024(1+r)5+DIV2025r(1+r)5 =$01.09+$11.092+$21.093+$2.31.094+$2.61.095+ ($2.60.09)1.095=$24.48 million$

Hence, the present value is $24.8 million.

Answer 14

b)

Expert Solution

Summary Introduction

To determine: Price per share

Explanation of Solution

Note:

Assume no debt, the share price are as follows,

$Price per share2019 = PV2019Number of shares= $24.4812= $2.04$

Hence, the price per share is $2.04.

Answer 15

b)

Expert Solution

Answer 16

b)

Expert Solution

Answer 17

Expert Solution

Answer 18

Summary Introduction

To determine: Price per share

Answer 19

Explanation of Solution

Note:

Assume no debt, the share price are as follows,

$Price per share2019 = PV2019Number of shares= $24.4812= $2.04$

Hence, the price per share is $2.04.

Answer 20

c)

Expert Solution

Summary Introduction

To confirm: The expected rate of return is 9%.

Explanation of Solution

Compute PV of the cash flows at various points in time:

$PV2020= $11.09+$21.092+ $2.31.093+$2.61.094+($2.60.09) 1.094= $26.68$

$PV2021= $21.09+$2.31.092+ $2.61.093+($2.6.09) 1.093= $28.09$

$PV2022= $2.31.09+$2.61.092+($2.6.09) 1.092= $28.61$

$PV2023= $2.6.09= $28.89$

$PV2024= $2.6.09= $28.89$

Compute rate of return using the formula $r0= (DIV1+P1–P0)P0$

$Rate of return2021= ($1+$28.09−$26.68)$26.68=0.09, or 9%$

$Rate of return2022= ($2+$28.61−$28.09)$28.09=0.09, or 9%$

$Rate of return2023= ($2.3+$28.89−$28.61)$28.61=0.09, or 9%$

$Rate of return2024= ($2.6+$28.89−$28.89)$28.89=0.09, or 9%$

Thus, the above calculation shows that the rate of return on Company P is exactly 9%.

Answer 21

c)

Expert Solution

Answer 22

c)

Expert Solution

Answer 23

Expert Solution

Answer 24

Summary Introduction

To confirm: The expected rate of return is 9%.

Answer 25

Explanation of Solution

Compute PV of the cash flows at various points in time:

$PV2020= $11.09+$21.092+ $2.31.093+$2.61.094+($2.60.09) 1.094= $26.68$

$PV2021= $21.09+$2.31.092+ $2.61.093+($2.6.09) 1.093= $28.09$

$PV2022= $2.31.09+$2.61.092+($2.6.09) 1.092= $28.61$

$PV2023= $2.6.09= $28.89$

$PV2024= $2.6.09= $28.89$

Compute rate of return using the formula $r0= (DIV1+P1–P0)P0$

$Rate of return2021= ($1+$28.09−$26.68)$26.68=0.09, or 9%$

$Rate of return2022= ($2+$28.61−$28.09)$28.09=0.09, or 9%$

$Rate of return2023= ($2.3+$28.89−$28.61)$28.61=0.09, or 9%$

$Rate of return2024= ($2.6+$28.89−$28.89)$28.89=0.09, or 9%$

Thus, the above calculation shows that the rate of return on Company P is exactly 9%.

Answer 26

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