Question
In: Accounting
Consider investments A and B with cash flows given below n A B 0 -30000 -30000...
Consider investments A and B with cash flows given below
|
n |
A |
B |
|
0 |
-30000 |
-30000 |
|
1 |
2000 |
11000 |
|
2 |
6000 |
10000 |
|
3 |
10000 |
10000 |
|
4 |
24000 |
8000 |
|
5 |
26000 |
5000 |
a) Find the IRR for each investment.
b) Find the incremental IRR, i.e., find IRR for B-A.
c) Plot the present worth of the cash flows of A and of B as a function of the interest rate, i.e., consister interest rates 5%,10%,15%,…, 40%. Identify the interest rate at which the two project have the same present worth. Observe that this interest rate is the same value as computed from the incremental IRR analysis.
Solutions
Expert Solution
a) A - 23.75% & B - 16.19% (use IRR formula in excel)
| N | A | B |
| 0 | -$30,000.00 | -$30,000.00 |
| 1 | $2,000.00 | $11,000.00 |
| 2 | $6,000.00 | $10,000.00 |
| 3 | $10,000.00 | $10,000.00 |
| 4 | $24,000.00 | $8,000.00 |
| 5 | $26,000.00 | $5,000.00 |
| IRR | 23.75% | 16.19% |
b) Incremental IRR B-A
= 16.19% - 23.75% = -7.56%
c)
Also in the last coloumn shown how by using IRR PW becomes Zero
At 40% interest rate PW of both project is near to same
| Disconting Factor | ||||||||||
| N | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% | PV @ 23.75% | PV @ 16.19% |
| 0 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 1 | 0.9524 | 0.9091 | 0.8696 | 0.8333 | 0.8000 | 0.7692 | 0.7407 | 0.7143 | 0.8081 | 0.8607 |
| 2 | 0.9070 | 0.8264 | 0.7561 | 0.6944 | 0.6400 | 0.5917 | 0.5487 | 0.5102 | 0.6530 | 0.7407 |
| 3 | 0.8638 | 0.7513 | 0.6575 | 0.5787 | 0.5120 | 0.4552 | 0.4064 | 0.3644 | 0.5277 | 0.6375 |
| 4 | 0.8227 | 0.6830 | 0.5718 | 0.4823 | 0.4096 | 0.3501 | 0.3011 | 0.2603 | 0.4264 | 0.5487 |
| 5 | 0.7835 | 0.6209 | 0.4972 | 0.4019 | 0.3277 | 0.2693 | 0.2230 | 0.1859 | 0.3446 | 0.4722 |
| Present Worth For Projec A under different discount % | ||||||||||
| Year | Cash Flow | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% | PW @ 23.75% |
| 0 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 |
| 1 | $2,000.00 | $1,904.76 | $1,818.18 | $1,739.13 | $1,666.67 | $1,600.00 | $1,538.46 | $1,481.48 | $1,428.57 | $1,616.16 |
| 2 | $6,000.00 | $5,442.18 | $4,958.68 | $4,536.86 | $4,166.67 | $3,840.00 | $3,550.30 | $3,292.18 | $3,061.22 | $3,917.97 |
| 3 | $10,000.00 | $8,638.38 | $7,513.15 | $6,575.16 | $5,787.04 | $5,120.00 | $4,551.66 | $4,064.42 | $3,644.31 | $5,276.72 |
| 4 | $24,000.00 | $19,744.86 | $16,392.32 | $13,722.08 | $11,574.07 | $9,830.40 | $8,403.07 | $7,225.64 | $6,247.40 | $10,233.65 |
| 5 | $26,000.00 | $20,371.68 | $16,143.95 | $12,926.60 | $10,448.82 | $8,519.68 | $7,002.56 | $5,798.35 | $4,834.30 | $8,958.75 |
| Total | $38,000.00 | $26,101.85 | $16,826.28 | $9,499.83 | $3,643.26 | -$1,089.92 | -$4,953.96 | -$8,137.93 | -$10,784.20 | $3.25 |
| IRR | 23.75% | |||||||||
| Present Worth For Projec B under different discount % | ||||||||||
| Year | B | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% | PW @ 16.19 % |
| 0 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 | -$30,000.00 |
| 1 | $11,000.00 | $10,476.19 | $10,000.00 | $9,565.22 | $9,166.67 | $8,800.00 | $8,461.54 | $8,148.15 | $7,857.14 | $9,467.25 |
| 2 | $10,000.00 | $9,070.29 | $8,264.46 | $7,561.44 | $6,944.44 | $6,400.00 | $5,917.16 | $5,486.97 | $5,102.04 | $7,407.34 |
| 3 | $10,000.00 | $8,638.38 | $7,513.15 | $6,575.16 | $5,787.04 | $5,120.00 | $4,551.66 | $4,064.42 | $3,644.31 | $6,375.20 |
| 4 | $8,000.00 | $6,581.62 | $5,464.11 | $4,574.03 | $3,858.02 | $3,276.80 | $2,801.02 | $2,408.55 | $2,082.47 | $4,389.50 |
| 5 | $5,000.00 | $3,917.63 | $3,104.61 | $2,485.88 | $2,009.39 | $1,638.40 | $1,346.65 | $1,115.07 | $929.67 | $2,361.16 |
| Total | $14,000.00 | $8,684.11 | $4,346.33 | $761.73 | -$2,234.44 | -$4,764.80 | -$6,921.97 | -$8,776.85 | -$10,384.36 | $0.46 |
| IRR | 16.19% |
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