Finance Question

Question

I am having trouble in a managerial accounting class.  If anyone could review the question and answer I have come up with, I would greatly appreciate it.

 

Your brother wants to borrow $10,000 from you. He has offered to pay you back $12,000 in a year. If the cost of capital of this investment opportunity is 10%, what is its NPV? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

NPV = Net Period Cash Flow / (1+r)^ T - Initial Investment
= 12,000 / (1 + 1.10) ^1 – 10000
= 12000 / 1.1 - 10000
= $909.09

Yes, this investment should be accepted.


IRR
=IRR(-10000: 12,000,10%) = 20% (from Excel)


For this investment, the IRR equals 20%. This is the interest rate that would be required to earn $12,000 on a $10,000 investment in 1 year when the NPV = 0. In this case, the IRR is positive, and the investment is expected to yield a positive return. The cost of capital can increase by 10% without changing the decision.

Answer 1

Your calculations and overall conclusions are correct! The investment has a positive NPV of $909.09, the IRR is 20%, and you should accept the investment at a 10% cost of capital. There are just a couple of small details worth clarifying.

Step 1: Calculate the Net Present Value (NPV).

NPV tells us how much value an investment creates today after accounting for the initial investment and the time value of money.

The formula is:

NPV = Future Cash Flow / (1 + r)^t - Initial Investment

Where:

1. Future Cash Flow = $12,000
2. r = 10% = 0.10
3. t = 1 year
4. Initial Investment = $10,000

Substitute the values:

NPV = 12,000 / (1 + 0.10)^1 - 10,000

NPV = 12,000 / 1.10 - 10,000

NPV = 10,909.09 - 10,000

NPV = $909.09

This means that after accounting for the required 10% return, lending your brother the money creates an additional $909.09 in value today.

One small correction: In your original formula, you wrote (1 + 1.10), but it should be (1 + 0.10). Your actual calculation correctly used 1.10.

Step 2: Should you accept the investment?

Yes!

The basic NPV decision rule is:

1. If NPV is positive, accept the investment.
2. If NPV is negative, reject the investment.
3. If NPV equals zero, the investment earns exactly the required return.

Since the NPV is positive $909.09, you should accept the investment, assuming your brother will repay the full $12,000 as promised and the 10% discount rate appropriately reflects the risk.

Step 3: Calculate the Internal Rate of Return (IRR).

IRR is the discount rate that makes the NPV of an investment equal to zero.

We start with the same NPV formula, but set NPV equal to zero:

0 = 12,000 / (1 + IRR) - 10,000

Add 10,000 to both sides:

10,000 = 12,000 / (1 + IRR)

Rearrange:

1 + IRR = 12,000 / 10,000

1 + IRR = 1.20

IRR = 1.20 - 1

IRR = 20%

This means the investment earns a 20% annual return.

We can also check this using a simpler calculation because the investment lasts exactly one year:

IRR = (12,000 - 10,000) / 10,000

IRR = 2,000 / 10,000 = 0.20 = 20%

Step 4: Determine the maximum allowable deviation in the cost of capital.

The estimated cost of capital is 10%, while the investment's IRR is 20%.

An investment is acceptable when its IRR is greater than its cost of capital.

Therefore:

Maximum allowable increase = IRR - Cost of Capital

= 20% - 10%

= 10 percentage points

The cost of capital can increase by up to 10 percentage points before the investment stops having a positive NPV.

For example:

1. At a 10% cost of capital, NPV = +$909.09. Accept.
2. At a 15% cost of capital, NPV = +$434.78. Accept.
3. At a 20% cost of capital, NPV = $0. Indifferent.
4. At a 25% cost of capital, NPV = -$400. Reject.

Technically, the cost of capital can increase by less than 10 percentage points while keeping the decision strictly favorable. At exactly 20%, the investment breaks even in present-value terms.

Final Answers:

1. NPV = $909.09
2. Accept the investment because NPV is positive.
3. IRR = 20%
4. Maximum allowable increase in the cost of capital = 10 percentage points, with 20% being the break-even rate.

Your original work was essentially correct. The main improvements are correcting the notation in the NPV formula and specifying that the allowable increase is 10 percentage points, rather than simply 10%, because those two expressions can mean different things.