How do i solve this question

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The Answer is B** I get the first part present value of current lease is $508,766.38, but i can’t calculate the present value of the lease being offered.**

PV of 5 annual payment of 120000 is total i 9 n 4 pmt 120000 388766 plus todays 120000 120000 fv 0 508766 ans. 508766 PV of 4 annual payment of 80000 is i 9 n 4 pmt 80000 259177 plus todays 200000 200000 fv 0 459177 ans. 459177 total savings = 508766-459177 49589

Easiest way is to take the difference in payments for years 1 through 4, which is $40,000 and discount them back using 9% (i.e., 1.09).

$40k/1.09 + $40k/1.09^2 +$40k/1.09^3 + $40k/1.09^4 =$129,589.

You sum those values to $129,589. So, she will save $129,589 in present value if she pays $80,000 (i.e., $200,000-$120,000) more upfront .

The difference between the immediate amount and eventual payments (in present value) is therefore: $129,589 - $80,000 or $49,589.

So she should take the deal.


Another maybe less easy way to think about it is:

Let’s say she doesn’t take the deal and saves the $80k upfront and invests it for a year at 9% at a cost of having to pay $40k each year.

Investing her $80k, at Y1 she will have $87,200 with which she can pay back the additional $40k she owes in Y1, leaving $47,200 in her pocket that she can reinvest.

In Y2, with revinvestment she will have an extra $51,448 in Y2 with which she can pay the additional $40k in Y2, leaving $11,448, which she can reinvest again

In Y3, with re-re-investment, she has $12,478 with which she can partially payback the Y3 $40,000 she owes, leaving her in the hole $27,521.

Now she has to pay interest on the money she owes , meaning in Y4 she will be down $29,998 AND owe the additional $40,000 ending up with -$69,998 in Y4 dollars.

Discount -$69,998 back 4 years ($69,998/1.09^4) and you get -$49,589 present value. So, it’s not a good idea for her not to take the deal.