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3 years ago

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A building owner charges net rent of $20 in the first year, $21 in the second year, and $22 in the third year. Using a 10 percen

t discount rate, what is the effective rent over the three years

1 answer:

Ronch [10]3 years ago

7 0

Answer:

$20.94

Explanation:

first we must determine the present value of the the 3 rent amounts:

PV = $20/1.1 + $21/1.1² + $22/1.1³ = 52.07

then you need to calculate the payment considering the following values:

principal = $52.07
n = 3
i = 10%

using a loan calculator payment = $20.9381 ≈ $20.94

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Instructions: Please make sure that you show all your work when solving the problems. Feel free to make any assumptions whenever

My name is Ann [436]

Answer:

Explanation:

From the given information:

The current price = $\dfrac{Dividend(D_o) \times (1+ Growth \ rate) }{\text{Cost of capital -Growth rate}}$

$15 = \dfrac{0.50 \times (1+ Growth rate)}{8\%-Growth rate}$

$15 \times (8 -Growth \ rate) = 0.50 +(0.50 \times growth \ rate)$

$1.20 - (15 \times Growth \ rate) = 0.50 + (0.50 \times growth \ rate)$

$0.70 = (15 \times growth \ rate) \\ \\ Growth \ rate = \dfrac{0.70}{15.50} \\ \\ Growth \ rate = 0.04516 \\ \\ Growth \ rate \simeq 4.52\% \\ \\$

2. The value of the stock

Calculate the earnings at the end of 5 years:

$Earnings (E_o) \times Dividend \ payout \ ratio = Dividend (D_o) \\ \\ Earnings (E_o) \times 35\% = \$0.50 \\ \\ Earnings (E_o) =\dfrac{\$0.50}{35\%} \\ \\ = \$1.42857$

$Earnings (E_5) year \ 5 = Earnings (E_o) \times (1 + Growth \ rate)^{no \ of \ years} \\ \\ Earnings (E_5) year \ 5 = \$1.42857 \times (1 + 12\%)^5 \\ \\ Earnings (E_5) year \ 5 = \$2.51763$

Terminal value year 5 = $\dfrac{Earnings (E_5) \times (1+ Growth \ rate)}{Interest \ rate - Growth \ rate}$

$=\dfrac{\$2.51763\times (1+0.04516)}{8\%-0.04516}$

=$75.526

Discount all potential future cash flows as follows to determine the stock's value:

$\text{Value of stock today} =\bigg( \sum \limits ^{\text{no of years}}_{year =1} \dfrac{Dividend (D_o) \times 1 +Growth rate ) ^{\text{no of years}}}{(1+ interest rate )^{no\ of\ years} }$

$+ \dfrac{Terminal\ Value }{(1+interest \ rate )^{no \ of \ years}} \Bigg)$

$\implies \bigg(\dfrac{\$0.50\times (1 + 12\%)^1) }{(1+ 8\%)^{1} }+ \dfrac{\$0.50\times (1+12\%)^2 }{(1+8\% )^{2}}+ \dfrac{\$0.50\times (1+12\%)^3 }{(1+8\% )^{3}} + \dfrac{\$0.50\times (1+12\%)^4 }{(1+8\% )^{4}} + \dfrac{\$0.50\times (1+12\%)^5 }{(1+8\% )^{5}} + \dfrac{\$75.526}{(1+8\% )^{5}} \bigg )$

$\implies \bigg(\dfrac{\$0.5600}{1.0800}+\dfrac{\$0.62720}{1.16640}+\dfrac{\$0.70246}{1.2597}+\dfrac{\$0.78676}{1.3605}+\dfrac{\$0.88117}{1.4693}+ \dfrac{\$75.526}{1.4693} \bigg)$

=$ 54.1945

As a result, the analysts value the stock at $54.20, which is below their own estimates.

3. The value of the stock

Calculate the earnings at the end of 5 years:

$Earnings (E_o) \times Dividend payout ratio = Dividend (D_o) \\ \\ Earnings (E_o) \times 35\% = \$0.50 \\ \\ Earnings (E_o) =\dfrac{\$0.50}{35\%}\\ \\ = \$1.42857$

$Earnings (E_5) year \ 5 = Earnings (E_o) \times (1 + Growth \ rate)^{no \ of \ years} \\ \\ Earnings (E_5) year \ 5 = \$1.42857 \times (1 + 12\%)^5 \\ \\ Earnings (E_5) year \ 5 = \$2.51763 \\ \\$

Terminal value year 5 = $\dfrac{Earnings (E_5) \times (1+ Growth \ rate)\times dividend \ payout \ ratio}{Interest \ rate - Growth \ rate}$

$=\dfrac{\$2.51763\times (1+ 7 \%) \times 20\%}{8\%-7\%}$

=$53.8773

Discount all potential cash flows as follows to determine the stock's value:

$\text{Value of stock today} =\bigg( \sum \limits ^{\text{no of years}}_{year =1} \dfrac{Dividend (D_o) \times 1 + Growth rate ) ^{\text{no of years}}}{(1+ interest rate )^{no \ of\ years} }+ \dfrac{Terminal \ Value }{(1+interest \ rate )^{no \ of \ years }} \bigg)$

$\implies \bigg( \dfrac{\$0.50\times (1 + 12\%)^1) }{(1+ 8\%)^{1} }+ \dfrac{\$0.50\times (1+12\%)^2 }{(1+8\% )^{2}}+ \dfrac{\$0.50\times (1+12\%)^3 }{(1+8\% )^{3}} + \dfrac{\$0.50\times (1+12\%)^4 }{(1+8\% )^{4}} + \dfrac{\$0.50\times (1+12\%)^5 }{(1+8\% )^{5}} + \dfrac{\$53.8773}{(1+8\% )^{5}} \bigg)$

$\implies \bigg (\dfrac{\$0.5600}{1.0800}+\dfrac{\$0.62720}{1.16640}+\dfrac{\$0.70246}{1.2597}+\dfrac{\$0.78676}{1.3605}+\dfrac{\$0.88117}{1.4693}+ \dfrac{\$53.8773}{1.4693} \bigg)$

=$39.460

As a result, the price is $39.460, and the other strategy would raise the value of the shareholders. Not this one, since paying a 100% dividend would result in a price of $54.20, which is higher than the current price.

Notice that the third question depicts the situation after 5 years, but the final decision will be the same since we are discounting in current terms. If compounding is used, the future value over 5 years is just the same as the first choice, which is the better option.

The presumption in the second portion is that after 5 years, the steady growth rate would be the same as measured in the first part (1).

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