# Answer to Question #33207 in Finance for 5656

Question #33207

Fabrice is looking to buy a new plug-in hybrid vehicle. The purchase price is $12,000 more than a similar conventional model. However, he will receive a $7,500 federal tax credit that he will realize at the end of the year. He estimates that he will save $1,200 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?( i.e, What is the DISCOUNTED payback period in years? Discount future cash flows before calculating payback and round to a whole year.)

Expert's answer

The purchase price is $12,000 more than a similar conventional model. However, he will receive a $7,500 federal tax credit.He will save $1,200 per year in gas over the conventional model. The cost of capital is 6%.

Payback Period = Initial Investment / Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:

Payback Period = A + B/C

In the above formula,

A is the last period with a negative cumulative cash flow;

B is the absolute value of cumulative cash flow at the end of the period A;

C is the total cash flow during the period after

So, Payback Period = 16 years.

Payback Period = Initial Investment / Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:

Payback Period = A + B/C

In the above formula,

A is the last period with a negative cumulative cash flow;

B is the absolute value of cumulative cash flow at the end of the period A;

C is the total cash flow during the period after

So, Payback Period = 16 years.

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