Question

2. What is the internal rate of return of a $10,000 investment that yields an annual benefit of $2400 for 5 years? Solve for the IRR 'by hand' by iterating between the interest rate tables in the back of the book.

Answer 1

Years	Cash flow in $	PVF@6%	PV of Cashflow in $	PVF@7%	PV of Cashflow in $
0	-10000	1	-10000	1	-10000
1	2400	0.9434	2264.16	0.9346	2243.04
2	2400	0.8900	2136	0.8734	2096.16
3	2400	0.8396	2015.04	0.8186	1964.64
4	2400	0.7921	1901.04	0.7629	1830.96
5	2400	0.7473	1793.52	0.7130	1711.2
		NPV at 6%=	109.76	NPV at 7% =	-154

Internal Rate of return (IRR) is the interest at which the NPV=0, to estimate it we have followed trial and error method, first we have taken the PV factor = 6%, where the NPV =$109.76, which is positive and then we have taken the PV factor = 7%, where the NPV = -$154 which is negative. So the Rate of return must fall in between 6% to 7%.

Therefore

R1 = 6%                               NPV1=$109.76

R2= 7%                 NPV2= -$154

Using linear interpolation method of estimation of Internal Rate of Return (IRR)

IRR= R1 + (R2-R1)X[NPV1/(NPV1-NPV2)]

IRR = 6 + (7-6)[(109.76)/ {109.76-(-154)}]

IRR = 6 + (7-6)[(109.76)/ (109.76+154)]

IRR = 6 + (7-6)[(109.76)/ (263.76)]

IRR = 6 + (1)[0.4161]

IRR = 6.4161    or   Approx 6.42%

The internal rate of return (IRR) is 6.42%