- 2070 Bhadra · 5 marks
Present equivalent of fuel costs, actual dollar
Short answer
Market rate i = 6%+5%+0.3%=11.3%. Inflated annual costs: 210,000, 220,500, 231,525, 243,101. Present worth at 11.3% = Rs 693,021 (equivalent to constant-dollar PW at 6%).
The annual fuel cost required to operate a small solid waste treatment plant are projected to be Rs. 200000 without considering any future inflation. The best estimate indicates that the annual inflation free interest rate i' will be 6% and the general inflation rate, f, will be 5%. If the plant has the remaining useful life of four years, what is the present equivalent of its fuel costs? Use actual dollar analysis.
Actual-dollar analysis converts the inflation-free (constant-dollar) cash flows into actual dollars and discounts them at the market interest rate.
Step 1: market interest rate
i = i' + f + i'f = 0.06 + 0.05 + (0.06)(0.05) = 11.3%
Step 2: actual-dollar fuel costs
Fuel cost in year n = 2,00,000(1.05)^n.
Step 3: present worth at 11.3%
| Year | Actual-dollar cost | (1.113)^−n | Present worth |
|---|---|---|---|
| 1 | 210,000 | 0.8985 | 188,679 |
| 2 | 220,500 | 0.8073 | 177,999 |
| 3 | 231,525 | 0.7253 | 167,924 |
| 4 | 243,101 | 0.6517 | 158,419 |
PW = 188,679 + 177,999 + 167,924 + 158,419 = Rs 693,021
Check: the same result comes from discounting constant dollars at i' = 6%: 2,00,000(P/A,6%,4) = 2,00,000(3.4651) = Rs 693,021. (The two agree because 200,000(1.05)^n/(1.113)^n = 200,000/(1.06)^n.)
Answer: The present equivalent of the fuel costs is Rs 693,021 (about Rs 6.93 lakh).
✓ Answer checked by Claude Opus 5.5 (high effort)
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