Question

Mustard's Inc. sold the rights to use one of its patented processes that will result in cash receipts of $2,500 at the end of each of the next four years and a lump sum receipt of $4,000 at the end of the fifth year. The total present value of these payments if interest is at 9% is:
a. $10,699.
b. $14,000.
c. $11,468.
d. $12,100.

Answer 1

Answer:

Option A is correct ($10,699)

Total Present Value=$10,699.03≅$10,699

Explanation:

Option A is correct ($10,699)

Amount Paid at end of each year=PMT=$2,500

Interest Rate=r=9%=0.09

Lump Sum amount=FV=$4,000

Formula for Present Value of Annuity (PVA)

$PVA=PMT(\frac{1-\frac{1}{(1+r)^n}}{r})$

Where:

n is the number of years=4 years

$PVA=\ 2,500(\frac{1-\frac{1}{(1+0.09)^4}}{0.09})\\ PVA=\ 8099.2997$

In case of Lump Sum:

$PV=FV(1+r)^{-n}$

Where:

n is the number of years=5 years

$PV=\ 4,000(1+0.09)^{-5}\\PV=\ 2599.7255$

So,

Total Present Value=PVA+PV

Total Present Value=$8099.2997+$2599.7255

Total Present Value=$10,699.03≅$10,699