Question

A $300,000 investment is made with anticipated cash flows of $65,000 a year for twelve years and a final payment of $261,100 in year thirteen.

a.) What is the expected return on this investment? b.) What would one pay for this investment and the end of year five assuming a required rate of return equals 21% and the expected cash flows are not expected to change? c.) What return would the seller earn? d.) Assume that expectations have changed at end of year five and cash flows will be $85,00/year in years 6 thru 12 and the terminal payment stays the same. What price would the buyer pay using 21% as the required rate of return. e.) What return would the seller earn? f.) What return would the buyer earn assuming the change cash flows does occur. g.) Briefly comment on how changes in expectations impact a buyer’s and seller’s rate of return.

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Answer 1

Let us assume the initial investment to be CFo = -300000 (negative sign because it is a cash inflow into the project)

Also assume expected Cash Flows from Year 1 to Year 12 to be CF1 .......... CF12 = 65000 in each year

Now assume the last Cash Out Flow expected in Year 13 to be CF13 = 261100

Part 1: Expected Return on this Investment

Expected return will be the IRR (Internal Rate of Return) which is the Discount Rate at which the NPV (Net Present Value) of the project equals to Zero.

IRR can be calculated using MS Excel or a Financial Calculator..

IRR = 21%

Part 2: What would one pay for this investment at the end of Year 5 assuming a Required Rate of Return of 21% and no change in expected cash flows

At the end of Year 5, any prospective buyer will be left with expected Cash Flows from Year 6 to Year12 of 65000 each and the last cash flow of 261100 from Year 13.

Now at the end of Year 5:

Year 6 will now be Year 1; Year 7 will now be Year 2 and so on, and Year 13 will be Year 8

So, CF1 to CF7 = 65000 each

CF8 = 261100

Now the amount which any buyer will pay for these cash flows will be the Sum of the Present Values of each of these cash flows calculated at a Discount Rate of 21%, which was given in the question.

Let us call the PV of Cash Flow in Year 1 to be PV1 and so on..

Present Values can be calculated as follows:

PV1 = CF1/(1+0.21)^1 = 65000/(1+0.21)^1 = 53719.00

PV2 = CF2/(1+0.21)^2 = 65000/(1+0.21)^2 = 44395.87

PV3 = CF3/(1+0.21)^3 = 65000/(1+0.21)^3 = 36690.81

PV4 = CF4/(1+0.21)^4 = 65000/(1+0.21)^4 = 30322.98

PV5 = CF5/(1+0.21)^5 = 65000/(1+0.21)^5 = 25060.31

PV6 = CF6/(1+0.21)^6 = 65000/(1+0.21)^6 = 20711.00

PV7 = CF7/(1+0.21)^7 = 65000/(1+0.21)^7 = 17116.53

PV8 = CF8/(1+0.21)^8 = 261100/(1+0.21)^8 = 56822.97

Adding all these present values above we will get = 284839.48

So, a buyer will pay $ 284839.48 for this investment at the end of Year 5.

Part 3: Return which the Seller would Earn

Initial Investment = 300000

At the end of Year 5, the amount a buyer will pay for the project =  284839.48

The Return for Seller = (284839.48 - 300000)/300000 = -5.05%

Part 4: Cash Flows change after Year 5, then what would be the amount a buyer will pay at a discount rate of 21%

Expected Cash Flows will change to $ 85000 per year from Year 6 through Year 12

Also given is that the terminal payment in Year 13 is unchanged..

To calculate the price a buyer would pay for this project at the end of Year 5 with new expected cash flows, we will adopt the same method which we did in Part 3 of this question. The only change will be in the Cash Flows from Year 6 through Year 12. We will replace the annual cash flow of 65000 with 85000, then we will calculate the PVs of each of these cash flows, and the resulting PV will be the amount a buyer would pay for this project at the end of Year 5.

The amount a buyer will pay at the end of Year 5 with new cash flows of 85000 per Year = $ 354998.41

Part 5: Return the Seller Would Earn

Initial Investment = 300000

At the end of Year 5, with change in expectations of the future Cash Flows, the amount a buyer will pay for the project =  354998.41

The Return for Seller = (354998.41 - 300000)/300000 = 18.33%

Part 6: Return earned by Buyer when Cash Flows Change

New Cash Flows are now like this:

CFo = -300000

CF1 through CF5 = 65000 each

CF6 through CF12 = 85000 each

CF13 = 261100

The IRR will be the return earned by the Buyer.

Calculating the IRR we will get:

IRR = 23%

Part 7:

As the expected cash flows change and it increases Year 6 onwards, the Expected Return for Buyer , which is the IRR, increases. The main reason is the greater cash flows which the buyer will bve getting in the future..

For the seller, with an increase in expected cash flows, his overall return increases because the Value which a buyer will pay to the seller at the end of Year 5 for this investment increases with the incraese in the expected cash flows.

Hopefully this will be helpful..