It is a third value.

The figures seem pretty unrealistic, so the inescapable conclusion is that

this is a homework question. Perhaps your child's? You have not given

enough information. The real question isn't whether the proposed house

investment is profitable, but whether it is more so or less so than the

existing bond investment. We assume you would cash in the bonds to pay

for the house, and would in addition take out a $240k loan.

NPV is a way of reducing future values to an equivalent "today" value,

but it is not always clear what rate of interest should be used in the

calculation. I think it makes sense to use (an estimate for) the rate

of general inflation. If you have $100k today, and stick it under the

mattress for a year, then inflation will reduce its future buying power.

This means that if you have $100k in 10 years' time, its equivalent

buying power today (which is basically what NPV means) would be $100k

divided by 1.03^10, which is roughly $74k.

The question really involves *four* interest rates. One is the 6% bond

investment rate (we assume profits are reinvested annually so that the

bonds will be worth $500k x 1.06^10 at the end of the 10 year period,

that's about $895k). A second is the loan interest rate at which you

will borrow the $240k, is this what you meant the 10% for? It seems a

bit high. A third is the general inflation rate to be used in the NPV

stuff, and 10% certainly seems excessive here. The fourth is the rate

at which the house value will increase (10% might have seemed reasonable

not very long ago, but it might be safer now to use the same value as

general inflation, or perhaps even a bit less).

You need to decide whether the loan is to be repaid over the 10 year

period in question, or longer. If longer, you need to consider how much

debt will be outstanding at the 10 year point, and use the NPV of that.

In any case you will need to deduct the loan payments from the rent

received.

A loan of $240k at 10%pa, repayable over 120 months, would cost £3115

per month. Your annual $50k rent corresponds to $4167 per month, and

so your net rent is only $1052 per month. The NPV of that (at 3%pa

inflation) is about $109k.

Let's say the house value goes up 2% per year (i.e. it depreciates about

1% in real terms, relative to 3% inflation), so will be worth about $902k

in 10 years; the NPV of that is about $671k.

Since the cost of the loan has been factored into the rent already, the

NPV of the house investment is $(109+671=780)k. The NPV of the *profit*

from the house investment (after deducting the $500k invested) is $280k.

The NPV of the bond investment is obtained from its future value ($895k)

reduced on the same NPV basis (3%) to about $666k, and hence the NPV of

its profit is only about $166k.

So the house investment is $114k more profitable than the bond investment,

but don't forget that you've not accounted for other expenses (loss of

rent when property empty, insurance, maintenance, repairs) which could

easily erode all of that and more.