- 2069 Bhadra · 4 marks
Feasibility of constant-dollar growing series
Short answer
Market interest rate i = i' + f + i'f = 5% + 8% + 0.4% = 13.4%. Discounting the growing constant-dollar series at i'=5% yields present worth of incomes $24,734. Since NPW = $24,734 - $20,000 = $4,734 > 0, the investment is feasible.
A series of five constant dollar (or real dollar) incomes (beginning with $5000 at the end of the first year) are increasing at the rate of 7% per year for five years. Inflation free interest rate is 5% and inflation is 8%. Is it feasible investment if investment cost is $20,000?
The incomes are in constant dollars, growing 7% a year: A_n = 5,000(1.07)^(n−1). The investment is made now, so it is an actual dollar amount of 20,000.
Market interest rate
i = i' + f + i'f = 0.05 + 0.08 + (0.05)(0.08) = 13.4%
Convert to actual dollars and discount at 13.4%
Actual income = constant income × (1.08)^n.
| Year | Constant $ | Actual $ = const × 1.08^n | (1.134)^−n | PW |
|---|---|---|---|---|
| 1 | 5,000 | 5,400 | 0.8818 | 4,762 |
| 2 | 5,350 | 6,240 | 0.7776 | 4,853 |
| 3 | 5,724 | 7,211 | 0.6857 | 4,945 |
| 4 | 6,125 | 8,333 | 0.6047 | 5,039 |
| 5 | 6,554 | 9,630 | 0.5333 | 5,135 |
PW of incomes = 24,734
NPW = −20,000 + 24,734 = 4,734
Check (constant dollars at i' = 5%): a growing series with g = 7% and i' = 5% gives PW = Σ 5,000(1.07)^(n−1)/(1.05)^n = (5,000/1.05) × [1 − (1.07/1.05)⁵] / [1 − 1.07/1.05] = 24,734, the same value.
Answer: PW of income = $24,734 > $20,000 (NPW = $4,734), so the investment is feasible.
✓ Answer checked by Claude Opus 5.5 (high effort)
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