Question

A building is expected to generate no cash flows for several years and then generate annual cash flows forever. What is the value of the building if the first annual cash flow is expected in 7 years, the first annual cash flow is expected to be 16,950 dollars, all subsequent annual cash flows are expected to be 1.29 percent higher than the cash flow generated in the previous year, and the cost of capital for the building is 8.68 percent?

Answer 1

For this, we need to calculate the Present Value of the cash flows (Step 1) and the Present Value of the Pertetual cash flows (step 2); Total of these two shall be the Present Value of the Building;

First Annual Cash Flow: $ 16950;

First Annual Cash Flow expected in Year 7;

Cost of Capital = 8.68%

(a) Hence, the Value of First Cash Flow in Year 7 = 16950 * 1/(1+8.68%)^7 = 16950 * 0.5584 = $ 9465.01

Perpertual Growth rate is 1.29%

(b) Hence, perpetual Value of the Cash Flows = (16950*(1+1.29%) / (8.68% - 1.29%) = 17168.66 / 7.39% = $ 232322.80

Present Value of the Perpetual Value = Perpetual Value * Discount factor at Year 7 = 232322.80 * 0.5584 = $ 129731.20

Total Value of the Building = (a) + (b) = Present Value of the Cash Flow + Present Value of the Perpetual Value = $ 9465.01 + $ 129731.20 = $ 139196.23

Answer: Present Value of the Building = $ 139196.23