Answer to Question #284802 in Microeconomics for Rose

Question

You have just been hired a consultant to help a firm to decide which of the three option to take to maximize the value of the firm over the next three years. The following table shows year end profits for each option. Interest rate are expected to be stable at 8 percent over the next three years.

Option A:

Year 1 year 2 year 3

$70,000 $80,000 $90,000

Option B:

Year 1 Year 2 year 3

$50,000 $90,000 $100,000

Option C:

Year 1 year 2 year 3

$30,000 $100,000 $115,000

a. Discuss the difference in the profits associated with each option

b. Which option has the greatest present value? Show computation

Answer 1

Solution:

PV =  $\sum \frac{FV}{(1 + r)^{t} }$

r = 8%

t = 3 years

Option A:

PV = $\frac{70,000}{(1 + 0.08)^{1} } + \frac{80,000}{(1 + 0.08)^{2} } + \frac{90,000}{(1 + 0.08)^{3} }$

= 75,600 + 93,312 + 113,374.08 = 282,286.08

PV = 282,286.08

 

Option B:

PV = $\frac{50,000}{(1 + 0.08)^{1} } + \frac{90,000}{(1 + 0.08)^{2} } + \frac{100,000}{(1 + 0.08)^{3} }$

= 54,000 + 97,200 + 179,712 = 330,912

PV = 330,912

 

Option C:

PV = $\frac{30,000}{(1 + 0.08)^{1} } + \frac{100,000}{(1 + 0.08)^{2} } + \frac{115,000}{(1 + 0.08)^{3} }$

= 32,400 + 116,640 + 114,866.88 = 293,906.88

PV = 293,906.88

 

b.). Option B has the greatest present value.