Question

1. You have plenty of cash to invest. You are considering an investment of $125,000 in a project which is expected to earn $14425 a year for ten years. Is it an attractive investment if your minimum expected annual rate of return is 5% (compound interest)? Calculate the expected annual rate of return (R) of the project. (6 points) (NO TABLES ONLY HAND CALCULATION) As well explain which equation you have used

Answer 1

As per the information given in the question

Initial investment of the project (I) =$125000

Annual expected income (A) =14425

Effective lift of the project (N) =10 years

Minimum expected annual rate of return or MARR =5%

Annual expected rate of return (ROR)=?

To calculate ROR of the project we have followed trial and error method

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

Years (N)	Cash flow	PVF@2%	PV of Cashflow	PVF@3%	PV of Cashflow
0	-125000	1	-125000	1	-125000.00
1	14425	0.980392	14142.16	0.970874	14004.85
2	14425	0.961169	13864.86	0.942596	13596.95
3	14425	0.942322	13593.00	0.915142	13200.92
4	14425	0.923845	13326.47	0.888487	12816.43
5	14425	0.905731	13065.17	0.862609	12443.13
6	14425	0.887971	12808.99	0.837484	12080.71
7	14425	0.870560	12557.83	0.813092	11728.85
8	14425	0.853490	12311.60	0.789409	11387.23
9	14425	0.836755	12070.19	0.766417	11055.56
10	14425	0.820348	11833.52	0.744094	10733.55
		NPV at 2%	4573.79	NPV at 3%=	-1951.82

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 = 2%, where the NPV =$4573.79, which is positive and then we have taken the PV factor = 3%, where the NPV = -$1951.82 which is negative. So the Rate of return must fall in between 2% to 3%.

Therefore

R1 = 2%                               NPV1=$4573.79

R2= 3%                 NPV2=-$1951.82

Using linear interpolation method of estimation of Rate of Return

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

ROR = 2 + (3-2)[(4573.79)/ {4573.79-(-1951.82)}]

ROR = 2 + (1)[(4573.79)/(4573.79+1951.82)]

ROR = 2 + (1)[(4573.79)/(6525.61)]=2+0.7009 =2.7009   or Approx 2.7%

The annual rate of return is approx 2.7%

Since ROR =2.7% < MARR(5%), it is not a attractive project for investment