Jill buys a house for $900k, lives there for exactly 10 years and sells it. Suppose Jill’s annual cost of ownership is exactly equal to the annual rent she would have paid to live in the same house. Suppose the price of Jill’s house grows 3.4% annually. Compute Jill’s annual IRR from owning net of renting

IRR is 3.40%

Explanation:

The cost incurred in acquiring the house in year zero is $900,000

But at the end of year ten the property would have appreciated to a higher value which can be computed using future value formula

FV=PV*(!+r)^N

PV is the cost of the property at $900,000

N is the number of years of owning the house which is 10 years

r is the rate of return on the property at 3.4%

FV=$900,000*(1+3.4%)^10

FV=$ 1,257,326.00  

However the IRR can be computed thus, note that zero inflow would be received from year 1 to 9

Years             Cash flow

0                   -900,000

1                         0

2                        0

3                        0

4                        0

5                        0

6                        0

7                       0

8                       0

9                      0

10        1,257,326.00  

IRR(values)

IRR is 3.40% as shown in the attached.

ANSWER:

1) The IRR is zero, because the price value of the house does not change, as the annual cost of ownership from the first year would be the same if she has paid rent for the house in 10 years time. Therefore the price value of the house from the first year to the 10th years will remain the same at $900,000

2) The annual IRR is 3.5%. That means that the price value of renting the house increases annually, and the price value for renting the house will increase with a rate of 3.4% yearly. after 10 year will be $1,257,326.0. As the yearly price value is compute below.

EXPLANATION: The question is divided into two section.

1) The first sections says that, Suppose Jill’s annual cost of ownership is exactly equal to the annual rent she would have paid to live in the same house.

SOLUTION: Jill IRR will be zero because her annual cost of ownership is the same as what she could have been paying if she has rented the house. That means they is no increase or decrease in the price value of the house.

2) The second section says that, Suppose the price of Jill’s house grows 3.4% annually. Compute Jill’s annual IRR from owning net of renting.

SOLUTION:

To compute the annual IRR from the first year to the tenth year.

FV = PV(1 + !)^n

FV is the future value

PV is the present value

! is the growth rate = 0.034

n is the annual period of growth = 1

Therefore; since the annual growth rate from the first year to the tenth year. The price value of the house for each house is as follows:

1st year:

FV = $900,000(1+0.034)^1 = $930,600

2nd year:

FV = $930,600(1.034) = $962,240.4

3rd year:

FV = $962,240.4(1.034) = $994,956.6

4th year:

FV = $995,956.6(1.034) = $1,028,785.1

5th year:

FV = $1,028,785.1(1.034) = $1,063,763.8

6th year:

FV = $1,063,763.8(1.034) = $1,099,931.8

7th year:

FV = $1,099,931.8(1.034) = $1,137,329.4

8th year:

FV = $1,137,329.4(1.034) = $1,175,998.6

9th year:

FV = 1,175,998.6(1.034) = $1,215,982.6

10th year:

FV = $1,215,982.6(1.034) = $1,257,326.0

Therefore the price value of the house after ten years will be $1,257,326.0

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