Question

KORONA Manufacturing is considering investing in either of two mutually exclusive projects, A and B. The firm has a 14 percent cost of capital, and the risk-free rate is currently 9 percent. The initial investment, expected cash inflows, and certainty equivalent factors associated with each of the projects are shown in the following table.

Project A
Project B

Initial investment (II)
$ 40,000
$ 56,000

Year (t)
Cash inflows (CFt)
Certainty equivalent factors (αt)
Cash inflows (CFt)
Certainty equivalent factors (αt)

   1
    $20,000                                             
            0.90                        
   $20,000             
          0.95

   2
      16,000                         
            0.80                    
     25,000             
          0.90

   3
      12,000                        
            0.60                       
     15,000                   
          0.85

   4                                     
      10,000
            0.50                    
     20,000                      
          0.80

   5
      10,000                            
            0.40                 
     10,000               
          0.80

Find the net present value (unadjusted for risk) for each project.
Find the certainty equivalent net present value for each project
Compare and discuss your findings in a) and b) above. Which, if either, of the projects do you recommend that the firm accept? Explain. (

Answer 1

a)

The Net present value is calculated by NPV function in excel => Initial Investment + NPV(0.14. Cash-flows year1-5)

Here, the discount rate is 0.14 or 14% which is the cost of capital of the firm

Year	Project A	Project B
0	-40000	-56000
1	20000	20000
2	16000	25000
3	12000	15000
4	10000	20000
5	10000	10000
NPV	$9,069.49	$7,940.41

Hence the NPV for project A = $9069.49 and NPV for project B = $7940.41

b)

Certainty equivalent cash-flows are obtained by multiplying cash-flows with Certainty equivalent factors

Year	Project A Cashflows	Certainty equivalent factors	Project A Certainty equivalent cash-flows
0	-40000	1	-40000
1	20000	0.9	18000
2	16000	0.8	12800
3	12000	0.6	7200
4	10000	0.5	5000
5	10000	0.4	4000

Year	Project B Cashflows	Certainty equivalent factors	Project B Certainty equivalent cash-flows
0	-56000	1	-56000
1	20000	0.95	19000
2	25000	0.9	22500
3	15000	0.85	12750
4	20000	0.8	16000
5	10000	0.8	8000

Calculating the NPV of certainty equivalent cash-flows using NPV similar to part a)

	Certainty equivalent cash-flows
Year	Project A	Project B
0	-40000	-56000
1	18000	19000
2	12800	22500
3	7200	12750
4	5000	16000
5	4000	8000
NPV	($4,463.67)	$213.81

Certainty equivalent NPV for Project A = -$4463.67 and for Project B = $213.81

c)

If the certainty factor is not taken (unadjusted for risk) into consideration (Part a), NPV of project A is higher than Project B suggesting Project A is more profitable.

However, when the cash-flows are adjusted for risk through the certainty factor (Part b), NPV of Project B is higher than that of Project A.

Hence, after considering the risk associated with cash-flows, Project B must be accepted by the firm.