Question

8. An investor has the opportunity to invest in the following project. The cash flows over a period of 5 years are shown in the table below Calculate the Internal Rate of Return (IRR) Use values of 7 % and 9 % as trial values Year Receipts (AED) Payments (AED) 400,000 Net Cash Flow (AED) (400 000) 100,000 100,000 100,000 100,000 100,000 0 1 100,000 100,000 100,000 100,000 100,000 2 3 4 5

Answer 1

I shall use interpolation method.

Cash inflows are in the form of uniform annuity.So,

NPV=-40000+10000*(P/A,i,5)

Here, we need to find i such that NPV=0

So, Let us calculate the value of NPV at i=7% and i=9%

First we calculate interest factors

$(P/A,i,n)=\frac{1-\frac{1}{(1+i)^{n}}}{i}$

$(P/A,0.07,5)=\frac{1-\frac{1}{(1+0.07)^{5}}}{0.07}=4.10019744$

$(P/A,0.09,5)=\frac{1-\frac{1}{(1+0.09)^{5}}}{0.09}=3.88965126$

NPV at i=7%

NPV (7%)=-400000+100000*(P/A,i,5)=-400000+100000*4.10019744=$10019.74

NPV at i=9%

NPV (7%)=-400000+100000*(P/A,i,5)=-400000+100000*3.88965126=-$11034.87

So,

Lower interest rate=L=7%

Higher interest rate=H=9%

NPV(L)=10019.74

NPV(H)=-11034.87

Interpolation gives us

IRR=L+(NPV(L)/ (NPV(L)-NPV(H))X(H-L)

IRR=7%+(10019.74/(10019.74+11034.87))*(9%-7%)=7.95%

Interpolation method gives us

IRR=7.95%

(If we use MS Excel or financial calculators, we can get more accurate IRR. It is 7.93%)