Question

An ordinary annuity that pays $300 per year has a present value of $21,000. Assuming a cost of capital of 6%, how much would this value change if it were an annuity due?

Round your answer to 2 decimal places.

You need a new car and are considering leasing versus buying.

Lease Option: You could lease the car for 6 years starting today for $6,000 per year with the first payment being due at the end of year 1.

Purchase Option: You could purchase the vehicle today for $36,000 and resell it at the end of 6 years for $5,000.

If the cost of capital is 4%, what option would you select and why?

Answer 1

To convert annuity ordinary to annuity due, we need to multiply the PV of ordinary annuity with (1+i)

So, PV of annuity due = 21000* 1.06 = $22260

Lease Option:

Year	Cash outflow	Present value @ 4%
1	6000	5,769
2	6000	5,547
3	6000	5,334
4	6000	5,129
5	6000	4,932
6	6000	4,742

Total PV of cash outflow under this option would be $31453

However if it is purchased, the initial outlfow = $36000

Salvage value at the end of 6 years = $5000

PV of the salvage value = 5000 * 0.790315= $3952

Therefore, the net outlfow= $36000- $3952 = $32048

Comparing the 2 options, we see that the total outflow is lower in Lease option. hence, we chose to lease.