Question

Find the rate of return for the following cash flow. Year Cash Flow -$25,000 15.000 -4.000 8.000 | 15,000 14

Answer 1

To calculate rate of return (ROR) in the problem we have followed trial and error method

Present Value factor (PVF) = (1+i)^-N

Years(N)	Cash flow	PVF@12% i=12%	PV of Cashflow	PVF@13% I=13%	PV of Cashflow
0	-25000	1	-25000	1	-25000
1	15000	0.8928571	13392.8571	0.8849558	13274.3363
2	-4000	0.7971939	-3188.7755	0.7831467	-3132.5867
3	8000	0.7117802	5694.2420	0.6930502	5544.4013
4	15000	0.6355181	9532.7712	0.6133187	9199.7809
		NPV at 12%=	431.0948	NPV at 25%=	-114.0682

Rate of return (ROR) is the interest rate at which the NPV=0, to estimate it we have followed trial and error method, first we have taken the PV factor = 12%, where the NPV =$431.0948, which is positive and then we have taken the PV factor =13%, where the NPV = -$114.0682which is negative. So the Rate of return must fall in between 12% to 13%.

Therefore

R1 = 12%                             NPV1=$431.0948

R2= 13%                               NPV2=-$114.0682

Using linear interpolation method of estimation of Rate of Return

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

ROR = 12 + (13-12)[( 431.0948)/ {431.0948-(-114.0682)}]

ROR = 12 + (1)[( 431.0948)/ (431.0948+114.0682)

ROR = 12 + (1)[( 431.0948)/ (545.163) =12 +0.7907    or Approx 12.79%

The annual rate of return is approx 12.79%