Question

Suppose an investor invested $400 in a project that is expected to generate revenue of $440 a year later. The required rate of return is the minimum return an investor expects to achieve by investing in a project. The required rate of return is influenced by the following factors: the risk-free rate of return is 4% , the expected return from the market is 8%, and beta is 1.5.

5-     How much is the residual earnings?

6-     If the required rate of return (cost of capital) for the project is 12%, do you think the project is making a profit or loss? Explain your answer?

7-     If the project were to generate revenues of $448, how much is the residual earnings? (assume that the required rate of return for the project is 10 percent)

8-     If the project for one-period with an expected rate of return of 10 percent, what is the value of the project? (use the residual earnings model)

9-     If the project were expected to earn at a 12 percent rate, , what is the value of the project?

Answer 1

Solution 5
Risk-free rate	4%
Expected market return	8%
Beta	1.5
Required rate of return=	Risk free rate + Beta * (Martket return - Risk free rate)
Required rate of return=	4% + 1.5 * (8%-4%)
The required rate of return=	10.00%
Initial investment	$ 400.00
Year-end return	$ 440.00
Year return	$   40.00
Equity charge=	Initial investment * required rate
Equity charge=	400*10%
Equity charge=	$   40.00
Residual earnings=	Year return- Equity charge
Residual earnings=	40-40
Residual earnings=	$          -
Solution 6
Initial investment	$ 400.00
Year-end return	$ 440.00
Year return	$   40.00
Equity charge=	Initial investment * required rate
Equity charge=	400*12%
Equity charge=	$   48.00
Residual earnings=	Year return- Equity charge
Residual earnings=	40-48
Residual earnings=	$    (8.00)
As we can see that the residual earnings are negative, hence we can say the project is making a loss.
Solution 7
Initial investment	$ 400.00
Year-end return	$ 448.00
Year return	$   48.00
Equity charge=	Initial investment * required rate
Equity charge=	400*10%
Equity charge=	$   40.00
Residual earnings=	Year return- Equity charge
Residual earnings=	48-40
Residual earnings=	$      8.00
Solution 8
Initial investment	$ 400.00
Year-end return	$ 440.00
Year return	$   40.00
Equity charge=	Initial investment * required rate
Equity charge=	400*10%
Equity charge=	$   40.00
Residual earnings=	Year return- Equity charge
Residual earnings=	48-40
Residual earnings=	$          -
Project value=	Intial investment + Residual earnings/(1+Required return)
Project value=	400+0
Project value=	$ 400.00
Solution 9
Initial investment	$ 400.00
Year-end return	$ 440.00
Year return	$   40.00
Equity charge=	Initial investment * required rate
Equity charge=	400*12%
Equity charge=	$   48.00
Residual earnings=	Year return- Equity charge
Residual earnings=	48-40
Residual earnings=	$    (8.00)
Project value=	Intial investment + Residual earnings/(1+Required return)
Project value=	400+(-8)/(1+12%)
Project value=	$ 392.86