Fabrice is looking to buy a new plug-in hybrid vehicle. The purchase price is $1
ID: 2641879 • Letter: F
Question
Fabrice is looking to buy a new plug-in hybrid vehicle. The purchase price is $12,500 more than a similar conventional model. However, he will receive a $5,600 federal tax credit that he will realize at the end of the year. He estimates that he will save $1,300 per year in gas over the conventional model; these cash outflows can be assumed to occur at the end of the year. The cost of capital (or interest rate) for Fabrice is 6%. How long will Fabrice have to own the vehicle to justify the additional expense over the conventional model? In other words, what is the DISCOUNTED payback period in years? Discount future cash flows before calculating payback rounded UP to a whole year.
Explanation / Answer
Additional Purchase price = $ 12500
End of the year Realisation of federal tax = $ 5600
Yearly Savings over conventional model = $ 1300
Total annual savings = $ 6900
PV of Savings of Year 1 @ 0,943 {6900 * 0.943} = $ 6507 {@ 6% cost of capital}
PV of Savings of Year 2 @ 0.890 {6900 *0.890 ) = $ 6148
TOTAL PV of 2 year inflows = $12655 ie. slightly > 12500 (initial outflow)
Discounted Payback in Years -ie. to own the vehicle to justify the additional expenses=
No.of yrs.taken to recover /payback the initial investment/outflow =Slightly < 2 Years.
Alternate method of finding Dicounted Payback period
Discounted payback period
Takes into account the time value of money while calculating the payback period ie. return /recovery of the
investment made - considering all cash outflows & the resultant cash inflows at various time periods.
Here we need to compare the incremental cash outflow of $ 12500 with the total incremental inflows of $ 6900
giving time value to both ---to find out the no of years in which the additional investment can be recouped.
Where,
A = Last period with a negative discounted cumulative cash flow;
B = Absolute value of discounted cumulative cash flow at the end of the period A;
C = Discounted cash flow during the period after A.
Substituting in the above , we have
1 + Absolute value of - 5991 / 6141 ie. 1 + 0.9755
=1.98 years or 1 year 11 months
Year Cash flow PV Factor @ 6% Discounted Cash Flow Cumulative DCF 0 -12500 1.0000 -12500 -12500 1 6900 0.9434 6509 -5991 2 6900 0.8900 6141 150Related Questions
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