(1)
a. $52,125/$12,000 = 4.3438, so the payback is about 4 years.
b. Project K's discounted payback period is calculated as follows:
Annual
Discounted @12%
Period
Cash Flows
Cash Flows
Cumulative
0
($52,125)
($52,125.00)
($52,125.00)
1
12,000
10,714.80
(41,410.20)
2
12,000
9,566.40
(31,843.80)
3
12,000
8,541.60
(23,302.20)
4
12,000
7,626.00
(15,676.20)
5
12,000
6,808.80
(8,867.40)
6
12,000
6,079.20
(2,788.20)
7
12,000
5,427.60
2,639.40
8
12,000
4,846.80
7,486.20
The discounted payback period is 6 +
60
.
427
,
5
$
20
.
788
,
2
$
years, or 6.51 years.
Alternatively, since the annual cash flows are the same, one can divide $12,000 by 1.12
(the discount rate = 12%) to arrive at CF
1
and then continue to divide by 1.12 seven more
times to obtain the discounted cash flows (Column 3 values).
The remainder of the
analysis would be the same.
c. NPV = -$52,125 + $12,000[(1/i)-(1/(i*(1+i)
n
)]
= -$52,125 + $12,000[(1/0.12)-(1/(0.12*(1+0.12)
8
)]
= -$52,125 + $12,000(4.9676) = $7,486.20.
Financial calculator: Input the appropriate cash flows into the cash flow register, input I =
12, and then solve for NPV = $7,486.68.