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Mustard's Inc. sold the rights to use one of its patented processes that will result in cash receipts of $3,100 at the end of each of the next five years and a lump sum receipt of $4,600 at the end of the fourth year. The total present value of these payments if interest is at 9% is:

Respuesta :

Answer:

$15,316.69

Explanation:

Data provided in the question:

Interest rate = 9% = 0.09

Amount at the end of each year = $3,100

Lump sum receipt at the end of the fourth year = $4,600

Now,

Present Value = [ $3,100 × PVA(9%, 5 Years) ] + [ $4,600 × PV(9%,4 Year) ]

also,

PVA = [ 1 - ( 1 + r)⁻ⁿ] ÷ r

thus,

PVA(9%, 5 Years) = [ 1 - ( 1 + 0.09)⁻⁵] ÷ 0.09

= 3.88965

PV = ( 1 + r )⁻ⁿ

thus,

PV(9%,4 Year) = ( 1 + 0.09 )⁻⁴

= 70843

Therefore,

Present Value = $3,100 × 3.88965 + $4,600 × 0.70843

= $12,057.915 + $3258.778

= $15,316.69

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