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An investor owns an empty block of land that was bought for $3 million a few years ago, but could be sold at auction for $2 million now. The land has local government approval to be developed into either:Low-rise townhouses costing $11 million now (t=0) that can be rented for $2 million in the first year, paid at the end of that year (t=1), and then rent is expected to grow by 3% pa every year forever; orHigh rise apartments costing $180 million now (t=0) that can be rented for $25 million in the first year, paid at the end of that year (t=1), and then rent is expected to grow by 1% pa every year forever.The government will only allow a single development so the projects are mutually exclusive.These projects have the same risk and 12% pa required return. Both will be fully constructed in one year, at which point tenants will move in and pay rent annually in advance, with the growth rates given. Ignore all maintenance costs, tenant vacancies, taxes and so on. All answer options are rounded to 6 decimal places. Compare the two projects against selling the land. Which of the following statements is NOT correct?Question 6Select one:a.$9.222222 million is the NPV of the low-rise townhouses.b.18.384615% pa is the IRR of the low-rise townhouses.c.$45.272727 million is the NPV of the high-rise apartments.d.1% pa is the IRR of the high-rise apartments.e.The high-rise apartment project should be accepted.

Question

An investor owns an empty block of land that was bought for 3millionafewyearsago,butcouldbesoldatauctionfor3 million a few years ago, but could be sold at auction for 2 million now. The land has local government approval to be developed into either:Low-rise townhouses costing 11millionnow(t=0)thatcanberentedfor11 million now (t=0) that can be rented for 2 million in the first year, paid at the end of that year (t=1), and then rent is expected to grow by 3% pa every year forever; orHigh rise apartments costing 180millionnow(t=0)thatcanberentedfor180 million now (t=0) that can be rented for 25 million in the first year, paid at the end of that year (t=1), and then rent is expected to grow by 1% pa every year forever.The government will only allow a single development so the projects are mutually exclusive.These projects have the same risk and 12% pa required return. Both will be fully constructed in one year, at which point tenants will move in and pay rent annually in advance, with the growth rates given. Ignore all maintenance costs, tenant vacancies, taxes and so on. All answer options are rounded to 6 decimal places. Compare the two projects against selling the land. Which of the following statements is NOT correct?Question 6Select one:a.9.222222millionistheNPVofthelowrisetownhouses.b.18.3846159.222222 million is the NPV of the low-rise townhouses.b.18.384615% pa is the IRR of the low-rise townhouses.c.45.272727 million is the NPV of the high-rise apartments.d.1% pa is the IRR of the high-rise apartments.e.The high-rise apartment project should be accepted.

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Solution

The question is asking for the incorrect statement among the given options related to the investment scenario. To find the correct answer, we need to calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) for both the low-rise townhouses and high-rise apartments.

  1. For the low-rise townhouses: The initial investment is 11million.Thefirstyearsrentis11 million. The first year's rent is 2 million, which grows at 3% per annum. The required return is 12%. The formula for NPV is: NPV = ∑ [Rt / (1+i)^t] - C0 Where, Rt is the net cash inflow during the period t, i is the discount rate or return that could be earned on capital over the time period t, and C0 is the initial investment. Since the rent grows forever, this is a perpetuity. The formula for the present value of a growing perpetuity is: PV = D / (r - g), where D is the expected annual payment, r is the required return rate, and g is the growth rate. So, NPV = [2million/(0.120.03)]2 million / (0.12 - 0.03)] - 11 million = $9.222222 million The IRR is the rate at which the NPV equals zero. However, without a financial calculator or software, it's difficult to calculate. So, we can't confirm option b.

  2. For the high-rise apartments: The initial investment is 180million.Thefirstyearsrentis180 million. The first year's rent is 25 million, which grows at 1% per annum. The required return is 12%. Using the same formulas, NPV = [25million/(0.120.01)]25 million / (0.12 - 0.01)] - 180 million = $45.272727 million Again, the IRR is difficult to calculate without a financial calculator or software, so we can't confirm option d.

  3. Comparing the two projects: The high-rise apartments have a higher NPV, so they would be the better investment if the investor is looking to maximize NPV.

Based on these calculations, the incorrect statement is either b or d, as we can't confirm the IRR for either project.

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