R305: ch. 14
You are able to buy an investment today for $1,000 that gives you the right to receive $438 in each of the next three years. What is the internal rate of return on this investment?
This is simply a yield calculation problem. Like any time-value-of-money problem, we are given four inputs and are asked to solve for the fifth. In this case, we must solve for the interest rate as follows: N = 3 I =? PV = -1,000 PMT = 438 FV = 0 Solving this setup tells us the above loan yields a 15 percent return.
What amount invested at the end of each year at 10 percent annually will grow to $10,000 at the end of five years?
$1,637.97 use TVM: n=5, fv= 10,000, i/y = 10, pmt=?
How much would you pay today for the right to receive $80 at the end of 10 years if you can earn 15 percent interest on alternative investments of similar risk?
$19.77: use tvm, n = 10, i/y = 15, fv = 80, pv = ?
As the level of perceived risk increases
Values decrease and expected returns increase.
How much would you pay today to receive $50 in one year and $60 in the second year if you can earn 15 percent interest on alternative investments of similar risk?
$88.85, use cf, CF0 = 0, CF1 = 50, CF2= 60, i = 15, NPV =?
If you deposit $50 per month in a bank account at 10 percent annual interest (compounded monthly), how much will you have in your account at the end of the 12th year?
At a 10% discount rate, this series of payments, or annuity, will be worth $13,821.89 in 12 years., N = 144, I = 10/12, PV = 0, PMT = 50, FV = ?
If you deposit $1 at the end of each of the next ten years and these deposits earn interest at 10 percent compounded annually, what will the series of deposits be worth at the end of the 10th year?
At a 10% discount rate, this series of payments, or annuity, will be worth $15.94 in ten years.N = 10, I = 10, PV = 0, PMT = 1, FV = ?
Assume the total cost of a college education will be $310,000 when your infant child enters college in 18 years. How much you invest at the end of each month in order to accumulate the required $310,000 at the end of 18 years if your monthly investments earn an annual interest rate of 5 percent, compounded monthly?
N = 18 x 12, I/YR = 5/12, PV = 0, PMT = ?, FV = 310,000, Payment = $887.74
Suppose you are going to receive $10,000 per year for five years. The appropriate interest/discount rate is 11 percent. What is the present value of the payments if they are in the form of an ordinary annuity?
N = 5, I/YR = 11, PV = ?, PMT = 10,000, FV = 0, PV = $36,959 | What is the present value if the payments are an annuity due? PV = $41,024 | Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity?N = 5, I/YR = 11, PV = 0, PMT = 10,000, FV = ?, FV = $62,278, What if the payments are an annuity-due? FV = $69,129
You are trying to accumulate a $40,000 down payment to purchase a home. You can afford to save $1,000 per quarter. If these quarterly investments earn an annual rate of 7 percent, how many quarters will it take to reach your goal?
N = ?, I/YR = 7/4, PV = 0, PMT = -1,000, FV = 40,000, N = 30.57 quarters or 7.65 years
Assume an investment is priced at $5,000 and has the following income stream (year 1, $1,000; year 2, -$2,000; year 3, $3,000; and year 4, $3,000). Would an investor with a required rate of return of 15 percent be wise to invest at a price of $5,000?
No, because the investment has a net present value of -$1,954.91. use CF: cf0: -5000, cf1: 1000, cf2: -2000, cf3: 3000 f3:2
How much would you pay today for the right to receive nothing for the next 10 years and $300 a year for the following 10 years if you can earn 15 percent interest on alternative investments of similar risk?
$372.17, use CF CF0-10= 0, CF11 = 300 F11 = 10, i = 15, npv = ?
If a landowner purchased a vacant lot six years ago for $25,000, assuming no income or holding costs during the interim period, what price would the landowner need to receive today to yield a 10 percent annual return on the land investment?
$44,289.03, use tvm: N = 6, I/Y = 10, PV = -25,000, FV = ?
You are considering the purchase of a small income-producing property for $150,000 that is expected to produce the following net cash flows: $50,000 every year for four years
Assume your required internal rate of return on similar investments is 11 percent. What is the net present value of this investment opportunity? What is the going-in internal rate of return on this investment? Should you make the investment?, Using the cash flow function on a financial calculator and entering the information provided above, the NPV of this investment is $5,122.28. Alternatively, the NPV can be solved as follows:N = 4, I = 11 %, PV = ?, PMT = $50,000, FV = 0, The present value of this series of payments is $155,122.28. Subtracting the amount of the cash outflow at period zero ($150,000), the present value is also $5,122.28. The going-in IRR for this investment is 12.59%. Yes, you should make the investment.
What monthly deposit is required to accumulate $10,000 in eight years if the deposits earn an annual rate of 8 percent, compounded monthly?
Assuming an 8% discount rate and a future value of $10,000, the monthly amount required to be deposited is $74.70. N = 96, I = 8/12, PV = 0, PMT = ?, FV = $10,000
How much would you pay today for an investment that provides $1,000 at the end of the first year if your required rate of return is 10 percent? Now compute how much you would pay at 8 percent and 12 percent rates of return.
At 10%, an investor would be willing to pay $909.09., N = 1 I = 10, PV = ?, PMT = 0, FV = 1,000 | At 8%, an investor would be willing to pay $925.93. N = 1, I = 8, PV = ?, PMT = 0, FV = 1,000 | At 12%, an investor would be willing to pay $892.86. N = 1, I = 12, PV = ?, PMT = 0, FV = 1,000
If you purchase a parcel of land today for $25,000 and you expect it to appreciate 10 percent per year in value, how much will your land be worth 10 years from now assuming annual compounding?
At a 10% discount rate, the investment will be worth $64,843.56 in ten years. N = 10, I = 10, PV = -25,000, PMT = 0, FV = ?
A family trust will convey property to you in 15 years. If the property is expected to be worth $50,000 when you receive it, what is the present value of your interest, discounted at 10 percent annually?
At a 10% discount rate, the present value of this future payment is $11,969.60. N = 15, I = 10, PV = ?, PMT = 0, FV = 50,000
You are at retirement age and one of your benefit options is to accept an annual annuity of $75,000 for 15 years. The first payment would be received one year from today. What lump sum settlement, if paid today, would have the same present value as the $75,000 annual annuity? Assume a 10 percent annual discount rate.
At a 10% discount rate, the present value of this series of future payments is $570,455.96. This is the lump sum equivalent of receiving $75,000 for 15 years.N = 15, I = 10, PV = ?, PMT = 75,000, FV = 0
If someone pays you $1 a year for 20 years, what is the present value of the series of future payments discounted at 10 percent annually?
At a 10% discount rate, the present value of this series of future payments, or annuity, is $8.51.N = 20, I = 10, PV = ?, PMT = 1, FV = 0
If your parents purchased an endowment policy of $10,000 for you and the policy will mature in 12 years, how much is it worth today, discounted at 15 percent annually?
At a 15% discount rate, the present value of this future payment is $1,869.07. N = 12, I = 15, PV = ?, PMT = 0, FV = 10,000
Dr. Bob Jackson owns a parcel of land that a local farmer has offered to rent from Dr. Bob for the next 10 years. The farmer has offered to pay $20,000 today or an annuity of $3,200 at the end of each of the next 10 years. Which payment method should Dr. Jackson accept if his required rate of return is 10 percent?
Dr. Jackson should choose the payment method that maximizes his net present value. If he chooses the lump sum payment, the net present value is simply the $20,000 he will receive today. If he chooses the annuity plan, the net present value will be only $19,662.61. N = 10, I = 10 %, PV =?, PMT = 3,200, FV = 0, Therefore, Dr. Jackson should choose the lump sum payment of $20,000.
1Raw land at the edge of urban development that lacks the necessary permits for development is one of the most risky kinds of real estate investment. Defend or refute this assertion.
Evaluated against the two types of investment risk confronting real estate investors, uncertainty of costs and uncertainty of value, raw land lacking permitting can be viewed as the riskiest form of real estate investment. Raw land at the edge of urban development that lacks necessary permitting for development possesses a large degree of value uncertainty because the future cash flows are not established. The value of the land is typically dependent on future growth to create market potential that is not currently in existence. Additionally, the probability of this occurring is dependent on land use regulations and the actions of the local planning authority. The total cost required to acquire and develop the raw land is unknown at the time of purchase. Only urban redevelopment projects possess comparable cost uncertainty as raw land without permitting.
You are contemplating replacing your conventional hot water heater with a solar hot water heater system at a cost of $4,000. How should you define the potential benefits that you need to receive to justify the investment?
The potential benefit gained from this investment is a reduction in future utility costs. This purchase requires an analysis of the initial costs and the value of the future benefit received in the form of lower utility bills. The homeowner should consider whether to finance this $4,000 investment and, if so, how much to borrow. The homeowner should also analyze how financing this purchase impacts the present and future cash flows associated with the purchase of the solar hot water heating system.
Calculate the present value of the income stream given below assuming a discount rate of 8 percent. What happens to present value if the discount rate increases to 20 percent?Year 1: $3,000, 2: $4,000, 3: $6,000, 4: $1,000
This problem is solved by entering the annual income stream and discount rate into the cash flow registers of any standard financial calculator and solving for the net present value. Assuming an 8% discount rate, the income stream is valued at $11,705.16. Alternatively, if the discount rate is 20%, the value of the income stream will be $9,232.25.
12You want to buy a house for which the owner is asking $625,000. The only problem is that the house is leased to someone else with five years remaining on the lease. However, you like the house and believe it will be a good investment. How much should you pay for the house today if you could strike a bargain with the owner under which she would continue receiving all rental payments until the end of the five-year leasehold at which time you would obtain title and possession of the property? You believe the property will be worth the same in five years as it is worth today and that this future value should be discounted at a 10 percent annual rate.
This problem requires you to determine the present value of the house today if you are willing to purchase it for $625,000 five years from today. Using a 10% discount rate, the home is worth $388,075.83 today. N = 5, I = 10, PV = ?, PMT = 0, FV = 625,000
specific features of real estate investing
application of the DCF method to analyze potential investments, calculate mortgage payments, debt service
What is the present value of $500 received at the end of each of the next three years and $1,000 received at the end of the fourth year, assuming a required rate of return of 15 percent?
$1,713.37 use CF, CF0= 0, CF1 = 500 F1= 3, CF2 = 1000, i 15, NPV =?
What is the present value of the following series of cash flows discounted at 12 percent: $40,000 now; $50,000 at the end of the first year; $0 at the end of year the second year; $60,000 at the end of the third year; and $70,000 at the end of the fourth year?
$171,836 (without rounding, answer is $171,835.94), use CF: CF0 = 40000, cf1 = 50000, cf2 = 0, cf3= 60000, cf4 = 70000, i = 12, npv = ?
How much will a $50 deposit made today be worth in 20 years if interest is compounded annually at a rate of 10 percent?
$336.37: use tvm buttons, n= 20, i/y = 10, pv = -50, fv = ?
