Question

You have an opportunity to acquire a property from a bank. It’s offered for $200,000. You would have to spend:

(1) $10,500 on various acquisition-related expenses,

(2) An average of $2,000 per month during the next 12 months for repair costs, etc.

You would be able to receive a loan: 90 percent loan-to-value ratio, 8% annual interest, for 12 months, payable monthly (interest-only loan).

Your market research indicates that after you repair the property, it may sell for about $225,000 at the end of 1 year. In addition, you will probably have to pay about $3,000 in fees & selling expenses.

a. If you wanted to earn a 20% return, compounded monthly, do you believe that $200,000 would be a good investment? (Show and explain all necessary calculations.)

b. If not, what counter-offer would you have to make to the bank in order to achieve the 20% return? (Show and explain all necessary calculations.)

Answer 1

Solution a:

Property Value = $200,000

Loan Amount = $200,000*90% = $180,000

Acquisition related expense = $10,500

Initial Cash outflows = $10,500 + ($200000*10%) = $30,500

Monthly cash outflows = $2,000 + ($180,000*8%/12) = $3,200

Cash outflow at the end of year = $180,000

Present value of cash outflows at 1.666% (20/12) monthly rate of interest = $30,500 + ($3,200 * cumulative PV factor for 12 periods) + ($180,000 * PV factor at 12th period)

=$30,500 + (3200 * 10.7951) + ($180,000 * 0.8201) = $212,662

If we invest $212,662 for 1 year at 20% return then required amount after 1 year = $212,662 * cumulative compound factor of 12 periods at 1.66666% monthly rate

= $212,662 * 1.21939 = $259,318

Net recovery on sale after 1 year = $225,000 - $3,000 = $222,000

Hence recovery is lesser than required recovery @ 20% return, therefore this is not a good investment.

Solution b:

Let counter offer to be made to bank to achieve 20% return = X

Loan amount = 0.90X

Initial Cash outflows = $10,500 + 0.10X

Monthly Cash outflows = $2,000 + (0.90X*8%/12) = $2000 + 0.006X

Cash outflow at end of year = 0.90X

Present value of cash outflows at 1.666% (20/12) monthly rate of interest = $10,500 + 0.10X + [($2,000+0.006X) * cumulative PV factor for 12 periods] + ($0.90X * PV factor at 12th period)

=$10,500 + 0.10X + [(2000+0.006X) * 10.7951) + ($0.90X * 0.8201)

=$10,500 + 0.10X + $21,590 + 0.0648X + 0.7381X

=$32,090 + 0.9029X

If we invest ($32090+0.9029X) for 1 year at 20% return then required amount after 1 year = $222,000

($32,090 + 0.9029X)*1.21939 = $222,000

$39,130 + 1.101X = $222,000

X = $166,094

Therefore we should counter offer to bank for $166,094 for earning 20% return.