The manager of a company wishes to calculate present worth (P.W.) of a small project with estimated costs of ₹1,75,000 now and ₹35,000 per year for 5 years beginning 1 year from now, with increase of 10% per year thereafter for the next 10 years. The real interest rate is 12% per year. Calculate

Question

The manager of a company wishes to calculate present worth (P.W.) of a small project with estimated costs of ₹1,75,000 now and ₹35,000 per year for 5 years beginning 1 year from now, with increase of [latex]10\%[/latex] per year thereafter for the next 10 years. The real interest rate is [latex]12\%[/latex] per year. Calculate the present worth (a) without an adjustment for inflation and (b) considering inflation at a rate of [latex]8\%[/latex] per year.

Accepted Answer

(a) Figure 10.1 shows the cash flow diagram. The P.W. without an adjustment for inflation is found using i = [latex]12\%[/latex] and [latex]g = 10\%[/latex].

[latex]P.W. = – ₹1,75,000 – ₹35,000\left(P/A,12\% ,4\right) – \left\{\frac{₹35,000\left[1-\left(\frac{1.10}{1.12} \right) ^{11} \right] }{0.12-0.10} \right\}\left(P/F,12\%,4\right)[/latex]

[latex]= – ₹1,75,000 – ₹35,000\left(3.0373\right) – \left(₹3,14,645\right)\left(0.6355\right)[/latex]

[latex]P.W. = – ₹4,81,262[/latex]

To adjust for inflation, calculate the inflated interest rate [latex]i_{f}[/latex] :

[latex]i_{f} = i + f + if = 0.12 + 0.08 + (0.12)(0.08) = 0.2096[/latex]

[latex]P.W. = – ₹1,75,000 – ₹35,000\left(P/A,20.96\%,4\right) – \left\{\frac{₹35,000\left[1-\left(\frac{1.10}{1.2096} \right) ^{11} \right] }{0.2096-0.10} \right\}\left(P/F,20.96\%,4\right)[/latex]

[latex]= – ₹1,75,000 – ₹35,000\left(2.5431\right) – \left(₹2,07,007\right)\left(0.4675\right)[/latex]

[latex]P.W. = – ₹3,60,784[/latex]

It is clear from the result of the above example that the present value of future inflated rupees is reasonably less when inflation adjustment is considered. Thus, in a high-inflation economy, it is advantageous for the borrower to use future (inflated) rupees whenever possible to make payments to repay a loan.

Question 10.3: The manager of a company wishes to calculate present worth (...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions