Chapter 26, Problem 18QS

Requirement 1:

To determine

To compute:

Payback period of Investment

Answer to Problem 18QS

Solution:

Payback period of Investment = 5 years

Explanation:

Payback period of the investment is calculated as under −

  $Paybackperiod=\frac{InitialInvestment}{Annualnetcashinflow}$

Given,

• Initial investment = $ 80 million
• Annual net cash flows = $ 16 million

  $\begin{array}{l}Paybackperiod=\frac{InitialInvestment}{Annualnetcashinflow}\\ Paybackperiod=\frac{\$80million}{\$16milllion}\\ Paybackperiod=5years\end{array}$

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under −

  $\begin{array}{l}Totalpresentvalueofcashinflows=Annualnetcashinflows\\ XPresentvalueofAnnuity\left(PVAF\right)atagivenrateforagivennumberofyears\end{array}$

Now, for present value of cash inflows −

Given −

• Annual net cash inflow = $ 16 million
• Number of years = 8 years
• Interest rate or required rate = 8%
Total present value of cash inflows =

  $\begin{array}{l}Totalpresentvalueofcashinflows=Annualnetcashinflows\\ XPresentvalueofAnnuity\left(PVAF\right)atagivenrateforagivennumberofyears\end{array}$

  $\begin{array}{l}Totalpresentvalueofcashinflows=\$16millionX5.747\\ Totalpresentvalueofcashinflows=\$91.952million\end{array}$

Net present value of the investment will be calculated as under −

  $Netpresentvalue=Totalpresentvalueofcashinflows-InitialInvestment$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

  $\begin{array}{l}Netpresentvalue\text{ = \$ 91}\text{.952 million - \$ 80 million}\\ Netpresentvalue\text{ =}\$11.952million\end{array}$

Conclusion

Thus,the payback period of the investment = 5 years.

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Requirement 2:

To determine

To compute:

Net present value of the investment.

Answer to Problem 18QS

Solution:

Net present value of the investment = $11.952 million

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under −

  $\begin{array}{l}Totalpresentvalueofcashinflows=Annualnetcashinflows\\ XPresentvalueofAnnuity\left(PVAF\right)atagivenrateforagivennumberofyears\end{array}$

Now, for present value of cash inflows −

Given −

• Annual net cash inflow = $ 16 million
• Number of years = 8 years
• Interest rate or required rate = 8%
Total present value of cash inflows =

  $\begin{array}{l}Totalpresentvalueofcashinflows=Annualnetcashinflows\\ XPresentvalueofAnnuity\left(PVAF\right)atagivenrateforagivennumberofyears\end{array}$

  $\begin{array}{l}Totalpresentvalueofcashinflows=\$16millionX5.747\\ Totalpresentvalueofcashinflows=\$91.952million\end{array}$

Net present value of the investment will be calculated as under −

  $Netpresentvalue=Totalpresentvalueofcashinflows-InitialInvestment$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

  $\begin{array}{l}Netpresentvalue\text{ = \$ 91}\text{.952 million - \$ 80 million}\\ Netpresentvalue\text{ =}\$11.952million\end{array}$

Conclusion

Thus, the net present value of the investment = $ 11.952 million.

Note −The following PVAF table has been used for referring PVAF @ 8 % for 8 years.