Question

Problem 30.7: What is the internal rate of return of a project that requires an investment of $1,000,000 now, and returns $150,000 at the end of each of years 1 through 15?

Answer 1

Internal Rate of Return is a discounted rate at which NPV is equal to Zero. To find out IRR, we use trial an error method. Suppose IRR is 10%.

NPV

Cumulative discounting factor for 15 years at the rate 10%= 7.6061

Present value= 150000*7.6061=1140900

NPV=1140915-1000000

=140915

Since at the rate of 10% NPV is positive then we have to assume higher rate to go close to NPV Zero. Take rate 15%

NPV

Comulative discounting factor at 15% for 15 years is 5.8474

Present value=150000*5.8474=877110

NPV= 877110-1000000=(122890)

Since NPV become negetive. Its means IRR lies between 10% to 15%.

Now with the help of interpolation method we will find out IRR.

IRR= R1+(NPV1*(R1-R2)/(NPV1-NPV2)

= 0.10+(140915*(0.15-0.10)/({140915-(-122890)}

= 0.10+(7045.75)/263805

=0.10+0.0267

= 0.1267

or, 12.67%(Approx.) Ans

R1​,R2​=randomly selected discount rates

NPV1​=higher net present value

NPV2​=lower net present value​