Answer :
Answer
a-1 . The Present Value of the installment plan is $94.38.
We calculate the PV of $25 for each of the three following years with the following formula:
[tex] PV_{Annuity} = Constant Payment * PVIFA_{0.04,3}[/tex]
where
PVIFA = Present Value interest factor of an annuity of $1 at 4% for 3 years.
[tex] PVIFA_{0.04,3} = 2.77509103[/tex]
We can ascertain this in excel by using the syntax : =pv(0.04,3,-1).
In this syntax, 0.04 is the interest rate, 3 is number of periods and since the annuity is $1 we write 1. We need to put in -1 because otherwise, we'll get the answer as a negative number. This is because excel treats any Present Values as outflows, and records them as negative.
Substituting the values above in the preceding equation we get,
[tex] PV_{Annuity} = 25 * 2.77509103[/tex]
[tex] PV_{Annuity} = 69.3772758[/tex]
In order to find the Present Value of the installment plan, we need to add the down payment of $25. So,
[tex] PV_{instalment} = $25 + 69.3772758[/tex]
PV of instalment = $94.38
a-2. We get a 6% discount when we pay in full, so the purchase price of the product becomes:
[tex] Purchase price = 100 - (100*0.06)[/tex]
[tex] Purchase price = $94 (100 - 6)[/tex]
Since the purchase price of the pay in full plan is lesser than that of the installment plan, the pay in full plan is a better option.
b-1. The Present Value of the installment plan is $90.75.
Since the first instalment falls due only after one year, we calculate the PV of $25 each of four years with the following formula:
[tex] PV_{Annuity} = Constant Payment * PVIFA_{0.04,4}[/tex]
where
PVIFA = Present Value interest factor of an annuity of $1 at 4% for 4 years.
[tex] PVIFA_{0.04,4} = 3.62989522[/tex]
We can ascertain this in excel by using the syntax : =pv(0.04,4,-1).
Substituting the values above in the preceding equation we get,
[tex] PV_{Annuity} = 25 * 3.62989522[/tex]
[tex] PV_{Annuity} = 90.7473806[/tex]
b-2. In this case, the PV of the pay in full plan remains at $94 while that of the instalment plan falls to $90.75. Since the PV of the Instalment plan is lower, we'll choose the instalment plan.
