Question

In: Finance

Year 1 2 3 4 5 6 7 8 9 10 A 1 1.01 1.0201 1.0303...

Year

1

2

3

4

5

6

7

8

9

10

A

1

1.01

1.0201

1.0303

1.0406

1.0510

1.0615

1.0721

1.0829

12.0305

B

1

.9900

.9801

.9703

.9606

.9510

.9415

.9321

.9227

10.0487

Assume a purchase price of $10 Million for both properties.

(a) What is the expected total return (IRR) on a 10-year investment in each property? Use a

financial calculator or equation solver for this.

(b) If the 10% cap rate represents a fair market value for each property, then which property must

be the riskier investment, so that no mispricing has occurred?

(c) What is the approximate annual growth rate in operating cash flows for each building during

first nine years? This is simply the percentage-change in cash flows.

(d) How is the growth rate related to the cap rate and the investor's IRR in each property?

Assuming each property is priced at its required rate of return (i.e. making it NPV=0), what

general economic relationship discussed in class does this show?

Solutions

Expert Solution

Part (a)

Please see the table below. The cells highlighted in yellow contain your answers. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

Part (b)

Property B is a riskier investment. Cash flows are decreasing by 1% year on year. A property is valued based on cap rate using the following equaton:

Valuet = = NOIt=1 / Cap rate

The assumption is NOI will at least remain at this level (NOIt=1) in future. Hence, if we value the property B using cap rate, this particular assumption is violated in entirety. Hence, we run the risk of paying more for an asset generating lower NOI.

Part (c)

the approximate annual growth rate in operating cash flows for each building during first nine years:

Property A = 1.00%

Property B = - 1.00%

Please see the table and the snapshot of the model placed in part (a). These two rates have been calculated annually.

Part (d)

Higher the growth rate:

  • Lower should be the cap rate
  • Higher should be the IRR
  • In this case, Property A has higher growth rate and hence higher IRR (please see the model snapshot placed in part (a) of this answer.

This shows the general economic relationship:

Value of an asset today = Present value of all the cash flows it can generate in future.

jeff jeffy answered 3 months ago
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