Question

Calculate the Internal Rate of Return of each of the following potential investments and recommend whether or not to include them in the upcoming capital budget given that the firm’s cost of capital is 14.5%.

New Software:

• Initial Cost                         $25,000
• Training Cost                    $12,000
• Annual Cost Savings        $10,500
• Useful Life                        6 Years

Machine A or Machine B

Note: The key word here is “or”. One or the other machine must be bought. So, the analysis should be based on the incremental cash flows resulting from the more expensive alternative.

• Annual Production in units                                   40,000
• Cost of Machine A                                                $38,000
• Cost of Machine B                                                $32,000
• Unit Cost to Produce on Machine A                     $2.20
• Unit Cost to Produce on Machine B                     $2.22
• Useful Life                                                            12 Years

Answer 1

Calculation of IRR of the new software:

Cost at the begining(Initial cost+Training cost) =$37000

Annual Savings =$10000

We can calculate IRR by using Present value of annuity formula.

Present value of annuity=Anuity* PV factor of annuity@ 'r' rate of interest for 6 years

37000 = PV factor*10000

PV factor= 37000/10000

=3.7

Find 3.7 in 6^th year column oin PV of annuity table.

We do not get exact 3.7 instead we get 3.7845(before 15% rate) and 3.6847(before 16% rate).

Hence the rate shall be between 15% and 16%

Use interpolation method:

*(Higher Rate-Lower Rate) NPV at lower rate=[(Annual Saving*PV factor of annuity@15% 6years)-Investment] =[10000 * (1.15)^6-1/(1.15)^6*.15]-37000 =10000*3.784483-37000 =37844.93-37000 =844.83    NPV at Higher rate= [10000*(1.16)^6-1/(1.16)^6*.16]-37000 =10000*3.684736 =36847.36-37000 = -152.64 Now we can put the values in the formula as below: IRR=                                               *(16 -15)                                           =15+.847                                           =15.847% Lower rate=15% Higher rate=16% As the IRR 15.847% is more than cost of capital i.e.14.5% the project is acceptable.

Machine A or Machine B Decision:

Machine A is more expensive than machine B by $6000. (38000-32000)

Hence machine A can be accepted only if the Present value of incremental savings in machine A is more than it's incremental cost i.e.$6000.

Annual incremental savings[40000*(2.22-2.20)] = 800

Present value of annual incremental savings =Savings*PV factor of annuity at 14.5% 12 years

=800*5.538344

=4430.675

(-) Incremental cost (6000)

Net present value of incremental saving = -1569.32

As the net present value of incremental saving is negative, the excess cost of machine is not acceptable.

Hence Machine B has to be choosen.

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