# How do i solve this question

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.

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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.