Question

note: Answer should be A

8. The capitalized cost of a series of cash flows starting at the end of the first year with $7,500 and decreasing at the rate of 15% each year for the following 7 years is closest to . Note: The series of cash flows from year 1 to 8 repeats forever. MARR = 12%, compounded semi-annually. a) $40,359 b) $38,701 c) $39,760 d) $41,469 e) $4,976 f) $4,989 g) $51,260

Answer 1

First we estimate the effective discount rate.

Number of compounding in a year=c=2 (semi annual)

Semi annual MARR=r=12%/2=6%

Effective discount rate=i=(1+r)^c-1=(1+6%)^2-1=0.1236

Now let us calculate the PV of cash flows in year 1 through year 8

Cash Flow in year 1=R=$7500

Growth rate=g=-15%

Number of years=n=8

PV of growing annuity is given by

$PVg=\frac{R}{i-g}*\left [ 1-\frac{(1+g)^{n}}{(1+i)^{n})} \right ]$

7500 PV g = 0.1236 + 0.1 * 1- (1 – 0.15) (1 + 0.1236))) = 24471.91

Now we estimate the equivalent annual worth of cash flows

EAW=PVg*(A/P,0.1236,8)

We know that

(A/P,1,n) = 1 -

0.1236 (A/P, 0.1236,8) = 1 = 0.203841 (1+0.1236)

EAW=24471.91*0.203841=4988.38

Capitalized cost=EAW/i=4988.38/0.1236=$40359.06

Correct option is

a) $40,359