A 10-year project is expected to earn $346 900 after tax in its first year, and

Question

A 10-year project is expected to earn $346 900 after tax in its first year, and the annual amount is expected to grow through the life of the project at the inflation rate of 2.5% per annum. Your discount rate is 8.86% per annum.

(a) Calculate the PV of this project using real cash flows.

(b) Calculate the PV of this project using nominal cash flows. You should get the same present value. (Hint: This is a growing annuity. Either look up a formula for that, or recognise the growing annuity is the difference between two growing perpetuties and use the Gordon growth model for the growing perpetutities.)

Explanation / Answer

a. Real discount rate = (1+8.86%) / (1+2.5) - 1 = 6.2049%

Present value of real cash flows as of one year from now = 346,900 + 346,900 * (1-1/(1+6.2049%)^9) / 6.2049% = 2,685,508.11

So present value of real cashflows as of now = 2,685,508.11 / (1+8.86%) = 2,466,939

b. Present value of growing annuity of nominal cashflows = first payment / (r-g) * (1-((1+g)/(1+r))^n)

This is = 346,900 / (8.86%-2.5%) * (1-(1.025/1.0886)^10) = 2,466,939

Hope this helped ! Let me know in case of any queries.

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