ANSWER:
Given that,
Life = 5 years
The formula for the net present worth (PW) of the project is given as
PW(i) = – 10,500 + 2,000(P/F, i, 1) + 2,000(P/F, i, 2) + 4,000(P/F, i, 3) + 4,000(P/F, i, 4) + 4,000(P/F, i, 5)
PW(i) = – 10,500 + 2,000/(1 + i)1 + 2,000/(1 + i)2 + 4,000/(1 + i)3 + 4,000/(1 + i)4 + 4,000/(1 + i)5
When i =10%
PW(10%) = – 10,500 + 2,000(P/F, 10%, 1) + 2,000(P/F, 10%, 2) + 4,000(P/F, 10%, 3) + 4,000(P/F, 10%, 4) + 4,000(P/F, 10%, 5)
PW(10%) = – 10,500 + 2,000/(1 + 0.1)1 + 2,000/(1 + 0.1)2 + 4,000/(1 + 0.1)3 + 4,000/(1 + 0.1)4 + 4,000/(1 + 0.1)5
PW(10%) = – 10,500 + (2,000 × 0.9091) + (2,000 × 0.8264) + (4,000 × 0.7513) + (4,000 × 0.6830) + (4,000 × 0.6209)
PW(10%) = – 10,500 + 1,818.2 + 1,652.8 + 3,005.2 + 2,732 + 2,483.6
PW(10%) = – 10,500 + 11,691.8
PW(10%) = $1,191.8
When i =15%
PW(15%) = – 10,500 + 2,000(P/F, 15%, 1) + 2,000(P/F, 15%, 2) + 4,000(P/F, 15%, 3) + 4,000(P/F, 15%, 4) + 4,000(P/F, 15%, 5)
PW(15%) = – 10,500 + 2,000/(1 + 0.15)1 + 2,000/(1 + 0.15)2 + 4,000/(1 + 0.15)3 + 4,000/(1 + 0.15)4 + 4,000/(1 + 0.15)5
PW(15%) = – 10,500 + (2,000 × 0.8696) + (2,000 × 0.7561) + (4,000 × 0.6575) + (4,000 × 0.5718) + (4,000 × 0.4972)
PW(15%) = – 10,500 + 1,739.2 + 1,512.2 + 2,630 + 2,287.2 + 1,988.8
PW(15%) = – 10,500 + 10,157.4
PW(15%) = -$342.6
Therefore the rate of return of the P5 is
i = 10% + [(1,191.8 – 0)/(1,191.8 – (– 342.6))] × 5%
i = 10% + (1,191.8/1,534.4) × 5%
i = 10% + (0.77 × 5%)
i = 10% + 3.8
i = 13.8%
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