Question

Please analyze, from the perspective of finance, the choice of buying a house vs renting an apartment. To make a quantitative analysis, suppose you have collected the following information:

If you rent a 1,000 sq ft two-bedroom apartment in RTP area, your monthly rent will be $900. The apartment is in move-in condition. You won’t have any upfront expenses when you move in.

If you want to buy a house, a 2,000 sq ft three-bedroom townhouse in RTP area is sold at $200,000. To get your application for mortgage approved by a bank, you need to pay 20% down payment. In addition, there is $2,000 closing cost. Your mortgage bank gives you two offers for mortgage. Offer one is a 30-years fixed-rate mortgage at 3.88% APR. Offer two is a five-year floating-rate mortgage, ARM 5/1, at 2.88% interest rate.

**Take offer 2 if buying**

A townhouse owner needs to pay $80 HOA fee each month. In addition, the property tax and house insurance together are about 1.5% of house value.

In addition, you make the following assumptions to simplify the situation:

Suppose you will live in an apartment or a townhouse for five years only. After year five, you will either buy a larger single family house or move to another place. That means you need to resell your house at year five.

Currently, the US house market is close to bottom. So you expect in next five years, the market value of your house will increase the same as inflation rate. Based on the knowledge you’ve learned from economics courses, you think inflation rate might be around 3% in next five years. That implies your house value will increase at 3% each year.

The utility expense of a townhouse will be higher than that of an apartment. However, considering that the interest part of your monthly mortgage payment is tax-deductible, you simply assume the extra utility expense of a townhouse and the tax-saving due to mortgage interest expense are canceled out. That means you don’t need to consider utility when you do your quantitative analysis.

You will pay $6,000 transaction costs when you resell the house.

At time when you resell your house, your mortgage is not paid off yet. So you have to use the sales proceeds to pay off your mortgage first. You can find how much mortgage balance remains unpaid by checking the mortgage amortization table at www.bankrate.com. Go to this website, click “calculator/mortgage calculator”, then input your mortgage information and calculate monthly payment, lastly, click “amortization table”, you will find your mortgage balance at end of year five.

Your opportunity cost (required rate of return) is 8%

Based on the above information, do you want to buy a house? Why?

(Hint: this is a replacement capital budgeting decision. You need to calculate incremental cash flows between housing and renting and use incremental cash flows to calculate NPV).

Answer #1

Solution: One should buy own house since the net present value of incremental cash flows is positive in the option of buying the house. the orkings are given below:

INCREMENTAL CASH FLOWS IN BUYING:

YEAR | CASH FLOWS | PVF@8% | DCF |

0 | -40000-2000=-42000 | 1 | -42000 |

1 | -960-3000-2866*+900=-5926 | .926 | -5487.04 |

2 | -960-3090-2866*+900=-6016 | .857 | -5157.75 |

3 | -960-3183-2866*+900=-6109 | .794 | -4849.52 |

4 | -960-3278-2866*+900=-6204 | .735 | -4560.13 |

5 | -960-3377-2866*+900-6000+231855 | .681 | 149423.40 |

total | 87368.97 | ||

* | Monthly installment | ||

231855 in yr 5 is calculated as 200000+3%inf each year for 5 years 900 each year is rental saving 960 each year is HOA Payment 80*12=960 |

Five years ago, someone used her $40,000 saving to make a down
payment for a townhouse in RTP. The house is a three-bedroom
townhouse and sold for $200,000 when she bought it. After paying
down payment, she financed the house by borrowing a 30-year
mortgage. Mortgage interest rate is 4.25%. Right after closing, she
rent out the house for $1,800 per month. In addition to mortgage
payment and rent revenue, she listed the following information so
as to figure out...

3. Laurie has been renting an apartment for a few years and is
considering buying a house. Her gross annual income is $48 000.
Laurie finds a house she likes, with a cost of $145 000. She has
saved up enough money to cover the closing costs plus an additional
$25 000 for a down-payment.
b) The mortgage is amortized over 25 years, with an interest
rate of 7.25% /a, compounded semi-annually. Use the TVM Solver to
determine Laurie’s monthly...

Find a place to live in your preferred location.
a. Find a house available for purchase that is at least two
bedrooms. Calculate a monthly payment associated with a 30-year
fixed mortgage assuming you can make no down payment on this house.
(use interest rate of 3.435% and house price of $244,900)
b. Calculate how long it would take you to save a $10,000 down
payment for your house if you can invest 2% of your monthly
income(monthly income is...

The remaining Application Exercises deal with purchasing a
house. Assume that you are currently renting an apartment for
$1,040 per month and you have been considering buying a house. You
have saved $10,000 towards a down payment for the house.
A salesperson informs you that he has a new house for sale, where
the house and land were independently appraised at $200,000, but
are being sold by the builderatadiscountpriceof
$185,000.Thebuilderwantstogetridofthepropertyquicklybecausethehouseisthelastonetobesoldinthedevelopmentand
the builder is moving on to construction of a new...

Consider a 30‐year mortgage on at $400,000 house that requires
monthly payments and has an interest rate (APR) of 8% per year. You
have $ 50,000 in cash that you can use as a down payment on the
house, but you need to borrow the rest of the purchase
price.
a) What will your monthly payments be if you sign up for this
mortgage?
b) Suppose you sell the house after 10 years. How much will you
need to pay...

Suppose you are buying a house and have taken out a mortgage for
$250,000. The mortgage is a 30 year fixed rate mortgage with an APR
of 5.25%. What is your monthly mortgage payment?

You would like to buy a house that costs $ 350,000. You have
$50,000 in cash that you can put down on the house, but you need
to borrow the rest of the purchase price. The bank is offering you
a 30-year mortgage that requires annual payments and has an
interest rate of 9% per year. You can afford to pay only $28,320
per year. The bank agrees to allow you to pay this amount each
year, yet still borrow...

You would like to buy a house that costs
$350,000.
You have
$50,000
in cash that you can put down on the house, but you need to
borrow the rest of the purchase price. The bank is offering you a
30-year mortgage that requires annual payments and has an interest
rate of
7%
per year. You can afford to pay only
$22,970
per year. The bank agrees to allow you to pay this amount each
year, yet still borrow
$300,000....

1.)
You
want to buy a house in Hermosa Beach CA, but you can only afford to
make monthly payments of $7,100. The interest rate on mortgages
right now is 4.25% p.a. with monthly compounding (APR), fixed for
30 years, with monthly payments. You have $155,000 saved to use as
a downpayment. What is the most that you can afford to pay for a
house (ignoring closing costs, property taxes, etc..)?
Answer: $1,598,265.76
2.)
Under
the same assumptions described in...

You plan to buy a house that has the sale price of $180,000. A
local bank can offer you a conventional 30-year mortgage with 20%
down payment and 4% APR. The bank also charge you 2% fees off the
loan amount, including origination fee, document fee and etc. How
much would be your upfront payment and monthly mortgage payment
(a) Upfront payment
(b) Monthly mortgage payment

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 20 minutes ago

asked 22 minutes ago

asked 23 minutes ago

asked 24 minutes ago

asked 35 minutes ago

asked 45 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago