Q37PGB
ExpertverifiedUsing payback, ARR, and NPV with unequal cash flows
Hughes Manufacturing, Inc. has a manufacturing machine that needs attention. The company is considering two options. Option 1 is to refurbish the current machine at a cost of $2,600,000. If refurbished, Hughes expects the machine to last another eight years and then have no residual value. Option 2 is to replace the machine at a cost of $3,800,000. A new machine would last 10 years and have no residual value. Hughes expects the following net cash inflows from the two options:
Year  Refurbish current machine  Purchase new machine 
1  $1,760,000  $2,970,000 
2  440,000  490,000 
3  360,000  410,000 
4  280,000  330,000 
5  200,000  250,000 
6  200,000  250,000 
7  200,000  250,000 
8  200,000  250,000 
9 
 250,000 
10 
 250,000 
Total  $3,640,000  $5,700,000 
Hughes uses straightline depreciation and requires an annual return of 10%.
Requirements
1. Compute the payback, the ARR, the NPV, and the profitability index of these two options.
2. Which option should Hughes choose? Why?
Method  Refurbish current machine  Purchase new machine 
Payback  3.86 years  3 years 
ARR  10%  10% 
NPV  $257,880  $581,520 
Profitability index  1.10  1.15 
2. The business entity must select the option of purchasing a new machine.
A capital budgeting metric that determines the time period in which the investment will give back the cash invested or the investment/cash recovery period is known as the payback period.
Calculation of payback period:
1. Refurbishment of current machine:
2. Purchase of new machine:
Working note:
Year  Refurbish current machine  Cumulative  Purchase new machine  Cumulative 
1  $1,760,000  $1,760,000  $2,970,000  $2,970,000 
2  440,000  $2,200,000  490,000  $3,460,000 
3  360,000  $2,560,000  410,000  $3,870,000 
4  280,000  $2,840,000  330,000 

5  200,000 
 250,000 

6  200,000 
 250,000 

7  200,000 
 250,000 

8  200,000 
 250,000 

9 

 250,000 

10 

 250,000 

Total  $3,640,000 
 $5,700,000 

Calculation of ARR:
Working note:
Particular  Amount $ 
Total net cash flows during the life of the project  $3,640,000 
Less: Total depreciation during the life of the asset  2,600,000 
Total operating income during the operating life  $1,040,000 
Asset operating life in years  8 
Average annual operating income  $130,000 
2. Purchase a new machine:
Working note:
Particular  Amount $ 
Total net cash flows during the life of the project  $5,700,000 
Less: Total depreciation during the life of the asset  3,800,000 
Total operating income during the operating life  $1,900,000 
Asset operating life in years  10 
Average annual operating income  $190,000 
Calculation of NPV:
Year  Refurbish current machine  X  Present value factor  =  Present value 
1  $1,760,000  X  0.909  =  $1,599,840 
2  440,000  X  0.826  =  $363,440 
3  360,000  X  0.751  =  $270,360 
4  280,000  X  0.683  =  $191,240 
5  200,000  X  0.621  =  $124,200 
6  200,000  X  0.564  =  $112,800 
7  200,000  X  0.513  =  $102,600 
8  200,000  X  0.467  =  $93,400 
Total present value of net cash inflow  $2,857,880  
Less: initial investment  (2,600,000)  
Net present value  $257,880 
2. Purchase of new machine:
Year  Purchase new machine  X  Present value factor  =  Present value 
1  $2,970,000  X  0.909  =  $2,699,730 
2  490,000  X  0.826  =  $404,740 
3  410,000  X  0.751  =  $307,910 
4  330,000  X  0.683  =  $225,390 
5  250,000  X  0.621  =  $155,250 
6  250,000  X  0.564  =  $141,000 
7  250,000  X  0.513  =  $128,250 
8  250,000  X  0.467  =  $116,750 
9  250,000  X  0.424  =  $106,000 
10  250,000  X  0.386  =  $96,500 
Total present value net cash inflow  $4,381,520  
Less: initial investment  (3,800,000)  
Net present value  $581,520 
Calculation of profitability index:
1. Refurbish current machine:
2. Purchase of new machine:
The business entity must purchase a new machine because its payback period is lower, and NPV and profitability index are higher than the current machine’s refurbishing.
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