A&B Enterprises is trying to select the best investment from among four alternat

Question

A&B Enterprises is trying to select the best investment from among four alternatives. Each alternative involves an initial outlay of $100,000. Their cash flows follow:

investment a - year 1 = 10k, year 2 = 20k, year 3 = 30k, year 4 = 40k, year 5 = 50k
investment b - year 1 = 50k, year 2 = 40k, year 3 = 30k, year 4 = 0, year 5 = 0
investment c - years 1-5 = 25k each
investment d - year 1 = 0, year 2 = 0, year 3 = 45k, year 4 = 55k, year 5 = 60k



Evaluate and rank each alternative based on a) payback period, b) net present value (use a 10% discount rate), and c) internal rate of return.

Explanation / Answer

Investment a)
Initial Outlay = $100,000
year 1 = 10k, year 2 = 20k, year 3 = 30k, year 4 = 40k, year 5 = 50k
Amount recovered in 4years = 10000+20000+30000+40000 =$100,000

Payback period = 4 years

NPV = -$100,000 + 10000/1.1+20000/1.1^2+30000/1.1^3+40000/1.1^4 +50000/1.1^5
= 6525.883105

IRR, NPV = 0
-$100,000 + 10000/(1+r)+20000/(1+r)^2+30000/(1+r)^3+40000/(1+r)^4 +50000/(1+r)^5 =0
r =12.01%

investment b - year 1 = 50k, year 2 = 40k, year 3 = 30k, year 4 = 0, year 5 = 0

Payback period = 2+ 10000/30000 = 2.333333

NPV = -$100,000 + 50000/1.1+40000/1.1^2+30000/1.1^3
= 1051.841

IRR, NPV = 0
-$100,000 + 50000/(1+r)+40000/(1+r)^2+30000/(1+r)^3 =0
r =10.65%

investment c - years 1-5 = 25k each

Amount recovered in 4years = 25000*4 = 100,000

Payback period = 4 years

NPV = -$100,000 + 25000/1.1+25000/1.1^2+25000/1.1^3+25000/1.1^4 +25000/1.1^5

       =-5230.330765

IRR, NPV = 0
-$100,000 + 25000/(1+r)+25000/(1+r)^2+25000/(1+r)^3+25000/(1+r)^4 +25000/(1+r)^5 =0
r =7.93%

investment d - year 1 = 0, year 2 = 0, year 3 = 45k, year 4 = 55k, year 5 = 60k

Amount recovered in 4years = 0+0+45000+55000 = 100,000

Payback period = 4 years

NPV = -$100,000 + 0/1.1+0/1.1^2+45000/1.1^3+55000/1.1^4 +60000/1.1^5

       =8630.185

IRR, NPV = 0
-$100,000 + 0/(1+r)+0/(1+r)^2+45000/(1+r)^3+55000/(1+r)^4 +60000/(1+r)^5 =0
r =12.29%

rank each alternative   from best to worst

a)payback period

Investment b > (Investment a, c, d = 4 years, all equal)

b) net present value

           d>a>b>c

c) IRR

   d>a>b>c

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