a)
1.
alternatives | present value |
10500 | 10500 |
5000 | 32576.11 |
61000 | 33179.96 |
formula
present value=cash flow/(1+r)n
n is the number of periods
r is the rate of return =7%
case 1-10500
10500 now
therfore n=0
cash flow=10500
r=7%
pv=10500/(1+0.07)0=10500
case 2-5000 a year for nine years
cashflow=5000
n=1 to 9
r=7%
pv=(5000/(1+0.07)1) + (5000/(1+0.07)2) + (5000/(1+0.07)3) + (5000/(1+0.07)4) + (5000/(1+0.07)5) + (5000/(1+0.07)6) + (5000/(1+0.07)7) + (5000/(1+0.07)8) + (5000/(1+0.07)9)
pv=4672.89+4367.19+4081.48+3814.47+3564.93+3331.71+3113.74+2910.04+2719.66 =32576.11
case 3- 61000 at the end of nine years
n=9
r=7%
cashflow=61000
pv=61000/(1+0.07)9=33179.96
2. 61000 at the end of nine years
the alternate with highest present value should be chosen. among these alternates case 3 has the highest present value and it should be taken.
b)
alternate | present value |
10500 | 10500 |
5000 | 31234.40 |
61000 | 30515.18 |
formula
present value=cash flow/(1+r)n
n is the number of periods
r is the rate of return =8%
case 1-10500
10500 now
therfore n=0
cash flow=10500
r=8%
pv=10500/(1+0.08)0=10500
case 2-5000 a year for nine years
cashflow=5000
n=1 to 9
r=8%
pv=(5000/(1+0.08)1) + (5000/(1+0.08)2) + (5000/(1+0.08)3) + (5000/(1+0.08)4) + (5000/(1+0.08)5) + (5000/(1+0.08)6) + (5000/(1+0.08)7) + (5000/(1+0.08)8) + (5000/(1+0.08)9)
pv=4629.63+4286.69+3969.16+3675.14+3402.91+3150.84+2917.45+2701.34+2501.24 =31234.40
case 3- 61000 at the end of nine years
n=9
r=8%
cashflow=61000
pv=61000/(1+0.08)9=30515.18
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