Question

Bill has been accepted into a university and is looking into his housing options.   He is considering purchasing a mobile home to live in for the 4 years he will be going to school.   The initial purchase price for the mobile home is $35,000.   To purchase the home, Bill will make a 15% down payment and borrow the rest of the principal with a 7 year, fully amortized loan at 10% interest. Luckily, Bill knows two friends from high school who are willing to be his roommates and pay $450 per month, each.   Bill figures that his lot rent will be $270 per month and taxes, utilities and insurance will be another $300 per month as well.   Bill’s roommates will not pay utilities.   Also, by buying the home, Bill will save $7,200 per year in rent, adding to his net returns.   After the four years, Bill hopes to sell the home for $20,000.   Assume straight-line depreciation over 9 years, a marginal tax rate of 25%, and an inflation rate of 2.5%. Bill requires a pre-tax rate of return of 10% and a risk premium of 2%.

1).What is the loan amount?

a.$35,000

b.$29,750

c.$31,500

d.$28,000

2). What are the tax savings from depreciation?

a.$1,000

b.$1,500

c.$972.22

d.$1,312.5

3). What are the tax savings from interest in year 1?

a.$567

b.$600

c.$743.75

d.$756

4). What is the yearly payment on the loan?

a.$11,160

b.$6,110.81

c.$5,563.33

d.$7,021.97

5). What is the book value of the loan after the four years?

a.$15,000

b.$15,196.69

c.$12,352.43

d.$14,082.44

6). What is Net Cash Flow after debt in year 1?

a.$31,500

b.$4,551.53

c.$4,184.41

d.$3,651.59

Please show all work for every question along with the formula that was used... Thanks!

Answer 1

Answering the first 4 sub-parts:

Answer for (1):

Mobile home purchase price = $35,000

Downpayment = 15% * $35000 = $5250

Loan amount = $35,000 - $5250 = $29,750 (Option B)

Answre for (2):

Mobile home purchase value = Asset Value = $35,000

Straight line depreciation for 9 years implies that the asset value is is depleted equally for 9 years. So, yearly depreciation is $35,000/9 = $3,888.89

As depreciation is a non-cash expense and is deducted from profit and loss account, Tax saved is $3888.89 * 25% (Tax rate) = $972.22 (Option C)

Answer for (3):

Loan Amount = $29,750 (Q1 answer)

Interest = $29,750*10% (Given interest rate) = $2,975

Tax saved by paying interest = $2,975 * 25%(Tax rate) = $743.75 (Option C)

Answer for (4)

Yearly payment on the loan can be found out by using PMT function in microsoft excel where in the detailed formula is =PMT(interest rate, number of installments, principal amount)

Or you can manually caluclate using the formula is P × r × (1 + r)^n/(((1 + r)^n) - 1) where P= Loan amount, r= interest rate, n=tenure

=$29,750 * 0.1 * (1+0.1)^7/((1+0.1)^7)-1

=$ 6,110.81 (Option B)