Annuities & Perpetuities: Understanding cash flow streams
A financial analyst is evaluating an investment that provides the following cash flows:
- A perpetuity that pays ₹10,000 annually, starting five years from today.
- An annuity due that pays ₹20,000 per year for 8 years, with payments starting immediately.
- A growing perpetuity that pays ₹5,000 in year 6, and grows at 3% per year indefinitely.
If the discount rate is 8% per annum, calculate the total present value of these cash flows today (Year 0).
Options:
A) ₹2,85,730
B) ₹3,12,450
C) ₹3,47,620
Anonymous Answered question 21 hours ago
Present Value Calculation of Cash Flows
1. Perpetuity (₹10,000 annually, starting in Year 5)
PV = C / r
PVYear 4 = 10,000 / 0.08 = 1,25,000
PVYear 4 = 10,000 / 0.08 = 1,25,000
Discounting to Year 0: PV = 1,25,000 / (1.08)^4 = 91,871
2. Annuity Due (₹20,000 for 8 years, starting immediately) : Using financial calculator:
- Set calculator to Annuity Due mode
- N = 8, I/Y = 8%, PMT = 20,000, FV = 0
- Compute PV → 1,24,065
3. Growing Perpetuity (₹5,000 in Year 6, growing at 3%)
PVYear 5 = C / (r – g) = 5,000 / (0.08 – 0.03) = 1,00,000
Discounting to Year 0:
PV = 1,00,000 / (1.08)^5 = 68,072
Total Present Value : PVTotal = 91,871 + 1,24,065 + 68,072 = 2,84,008
Closest option: ₹2,85,730
Answer: Option A
Author Changed status to publish 21 hours ago
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