# Is the investment profitable?

U

#### ulrik

I want to buy a house. The price is \$740.000. I already have \$500.000
(now invested in 6% bonds). I want to rent out the house. I think I
can get \$50.000 pr. year. My time horizon is 10 years. Is this
investment profitable for me?
I've read about the concept of Net Present Value etc., but I can't
figure it out.
Is the NPV = -740.000 + NPV(50.000 in 10 year) = -432.772 (with an
interest rate of 10%) OR is it
NPV = (-740.000+500.000) + NPV(50.000 in 10 years) = 67.228? Or is it
a third value?

Thank you!

R

#### Ronald Raygun

I want to buy a house. The price is \$740.000. I already have \$500.000
(now invested in 6% bonds). I want to rent out the house. I think I
can get \$50.000 pr. year. My time horizon is 10 years. Is this
investment profitable for me?
I've read about the concept of Net Present Value etc., but I can't
figure it out.
Is the NPV = -740.000 + NPV(50.000 in 10 year) = -432.772 (with an
interest rate of 10%) OR is it
NPV = (-740.000+500.000) + NPV(50.000 in 10 years) = 67.228? Or is it
a third value?
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

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

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.

U

#### ulrik

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

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

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.

Thank you very much!
This was a very nice and detailed explanation.
I admit it's a homework question, but I need to understand it.
I need to read it carefully some more times, but I think, I understand
the principles.
I don't think it should be "this hard" to answer/calculate the answer,
though.
Maybe I'm making it a bit to advanced/complicated I think, we were meant to use the Discounted Cash Flow method with one
"simple" equation like the one I tried to use above.
describe.

T

#### tim.....

I admit it's a homework question, but I need to understand it.
I need to read it carefully some more times, but I think, I understand
the principles.
I don't think it should be "this hard" to answer/calculate the answer,
though.
Of course homework questions have to be hard. If the were easy, parents
would be able to do them tim