Question

# Assume you have the following cash flow in actual dollars: Year 0 -\$163; Year 1 -\$95;...

Assume you have the following cash flow in actual dollars: Year 0 -\$163; Year 1 -\$95; Year 2 \$131; Year 3 \$120; Year 4 \$153. The general inflation rate is 2.4%. What is the inflation-free IRR of this cash flow? Express your answer as a percentage.

Inflation rate = 2.4%

Cash flow in year 0 = -\$163

Year 1 Cash flow in constant dollar = -95/1.024 = -\$92.77

Year 2 Cash flow in constant dollar = 131/1.024^2 = \$124.93

Year 3 Cash flow in constant dollar = 120/1.024^3 = \$111.76

Year 4 Cash flow in constant dollar = 153/1.024^4 = 139.15

Let, IRR = R

Then,

163 = -92.77/(1+R) + 124.93/(1+R)^2 + 111.76/(1+R)^3 + 139.15/(1+R)^4

At R = 15%

Present value of the cash inflows = \$166.839

At R = 16%

Present value of the cash inflows = \$161.32

Then as per the method of interpolation,

R = 15% + ((166.839 - 163)/( 166.839-161.32))*(16%-15%)

R = 15.69%

So, inflation free IRR is 15.69%.

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