Question

Convert the cash flows shown above (black arrows) into an equivalent annual worth "A" in years 1 through 8 (red arrows) at i = 15% per year. *solve it in Excel, show formula A = ? 9_19 21 31 41 51 of 71 81 i=15% VVVVV A = $9000 $9000 + $7000

Answer 1

ANSWER:

I = 15%

We will find the present worth of the cash flows and then the equivalent annual worth.

pw = cash flow from year 4 to 8(p/a,i,n)(p/f,i,n) + cash flow in year 6(p/f,i,n)

pw = 9,000(p/a,15%,5) (p/f,15%,3) + 7,000(p/f,15%,6)

pw = 9,000 * 3.352 * 0.6575 + 7,000 * 0.4323

pw = 19,835.46 + 3,026.1

pw = 22,861.56

aw = pw(a/p,i,n)

aw = 22,861.56(a/p,15%,8)

aw = 22,861.56 * 0.2229

aw = 5,095.842

so the equivalent annual worth is $5,095.842

year	1	2	3	4	5	6	7	8
cash flows	0	0	0	9000	9000	16000	9000	9000
npv	₹ 22,863.16
pmt	₹ 5,095.06

In excel we will use the npv formula for finding the npv (pw) =npv(rate,cash flow from year 1 to year 8)

=npv(15%,0,0,0,9000,9000,16000,9000,9000)

=22,863.16

now we will use the pmt formula to fidn the equivalent annual worth.

=-pmt(rate,nper,pv,fv,type)

rate = 15% , nper = 8 , pv = 22,863.16 , fv = 0 and type = 0

=-pmt(15%,8,22863.16)

=5,095.06

note that the difference between solving via excel and compounding factor tables of few decimals is due to full values being taken in excel.