Question

An investment is expected to generate annual cash flows forever. The first annual cash flow is expected in 1 year and all subsequent annual cash flows are expected to grow at a constant rate annually. We know that the cash flow expected in 2 year(s) from today is expected to be 1,860 dollars and the cash flow expected in 8 years from today is expected to be 3,140 dollars. What is the cash flow expected to be in 5 years from today?

Oxygen Optimization just bought a new filtration system for 165,900 dollars. To pay for the filtration system, the company took out a loan that requires Oxygen Optimization to pay the bank a special payment of 104,700 dollars in 2 year(s) and also make regular annual payments forever. The first regular payment is expected in 1 year and is expected to be 1,900 dollars. All subsequent regular payments are expected to increase by a constant rate each year forever. The interest rate on the loan is 16.93 percent per year. What is the annual growth rate of the regular payments expected to be? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Lola owns a(n) yoga studio that is worth 174,497 dollars and is expected to make annual cash flows forever. The cost of capital for the yoga studio is 9.78 percent. The next annual cash flow is expected in 1 year and is expected to be 10,400 dollars. All subsequent cash flows are expected to grow annually at a constant growth rate. What is the cash flow produced by the yoga studio in 5 years expected to be?

Mary owns two investments, A and B, that have a combined total value of 236,874 dollars. Investment A is expected to pay 8,581 dollars per year forever; its next payment is expected in 1 year; and its expected return is 4.32 percent per year. Investment B is also expected to make annual payments forever and make its next payment in 1 year. Investment B’s next payment is expected to be 3,694 and all subsequent payments are expected to grow by 5.22 percent per year forever. What is the annual expected return for investment B?  Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

You have asked four unrelated questions. I will answer the first one.

An investment is expected to generate annual cash flows forever. The first annual cash flow is expected in 1 year and all subsequent annual cash flows are expected to grow at a constant rate annually. We know that the cash flow expected in 2 year(s) from today is expected to be 1,860 dollars and the cash flow expected in 8 years from today is expected to be 3,140 dollars. What is the cash flow expected to be in 5 years from today?

Let's call the cash flow expected at the end of year "i" as C_i

Let's further assume that annual growth rate in the two successive cash flows is g.

Hence, C₂ = C₁ x (1 + g) = $ 1,860 -----------------Equation (1)

And, C₈ = C₁ x (1 + g)⁷ = $ 3,140 ------------------Equation (2)

We have to find, C₅ = C₁ x (1 + g)⁴

Multiply equation (1) with (2):

C₁ x (1 + g) x C₁ x (1 + g)⁷ = C₁² x (1 + g)⁸ = [C₁ x (1 + g)⁴]² = C₅² = 1,860 x 3,140 =  5,840,400
Hence, C₅

= $  2,416.69 = the cash flow expected to be in 5 years from today