# Question regarding present value with discount rate

I am a novice at finance subjects and need to find out Present value given a few details

The university fees of \$45,000 a year will have be paid starting 11 years from today. He is analysing an insurance plan that pays out \$45,000 a year for 4 years with the first payout 11 years from today. The insurance plan has several payment options:

Option 1 Pay \$60,000 today

Option 2 Beginning 1 year from today, pay \$12,000 a year for the next 8 years

Option 3 Beginning 1 year from today, make payments each year for the next 8 years. The first payment is \$11,000 and the amount increases by 5% each year

The question is asking to calculate Present Value for each option with a 10% discount rate.

I understand that PV = FV / (1 + r)^t

Am I right to say that FV is \$180,000, r is 0.1 and t is 11 years? And if so, Option 1 PV = \$180000 / 1.1^11 = \$63088.90

But I am stucked for Option 2 and 3, how do I move on from here?

Your answer for the PV of the insurance is not right. You need to discount each of the 4 payments separately since they occur at different times. So the total PV would be

``````  45,000 / (1.1)^11
+ 45,000 / (1.1)^12
+ 45,000 / (1.1)^13
+ 45,000 / (1.1)^14
--------------------
54,995
``````

For 2 and 3, find the PV of each option and compare it to the PV of the insurance plan. You'll need to calculate the PV of each cash flow separately. So the answer to #2 would be

``````  12,000 / (1.1)^1
+ 12,000 / (1.1)^2
+ 12,000 / (1.1)^3
...
``````

and 3 would be

``````  11,000            / (1.1)^1
+ 11,000 * (1.05)^1 / (1.1)^2
+ 11,000 * (1.05)^2 / (1.1)^3
...
``````
• I have calculated and obtained the following Option 1 - \$54995, Option 2 - \$64019, Option 3 - \$68366, since Option 1 has the lowest value, am I safe to say that John should choose Option 1 since the PV is lower hence translating to a higher discount? – JJ Lin Sep 24 at 10:20
• Actually Option 1 is "pay 60k now" but yes that is the cheapest option. The insurance is a required expense, so you'd pick the financing method that has the lowest current cost which would be Option 1. – D Stanley Sep 24 at 12:17
• So the value of \$54995 is just a calculated value and the real PV is \$60k for Option 1? – JJ Lin Sep 24 at 12:28
• The \$54,995 is the PV of the insurance contract. The three options are different ways to purchase that contract. You'd choose the one that has the lowest current cost. – D Stanley Sep 24 at 12:30