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Paulo plans to buy a holiday villa in five years’ time for cash. He estimates the cost will be $1.5m. He plans
to set aside the same amount of funds each year for five years, starting immediately and earning a rate of
10% interest per annum compound.
To the nearest $100, how much does he need to set aside each year?Can you please explain how to solve questions like these?
The present value of the $1.5M in 5 years time must be the same as the present value of the 5 years of equal payments.
The PV of the $1.5M is arrived at by multiplying by the 5 year PV factor.
The PV of the annual payment is arrived at by multiplying by (1 + the 4 year annuity factor) since the first payment is immediate.
Letting the annual payment be X and making the two PV’s equal lets you calculate the value of X.
I understand now. Do we always add the 1 to the annuity factor whenever the annuity cashflow start from time 0?
Yes, because the PV of a cash flow at time 0 is equal to the amount of the cash flow.
The annuity factors from the tables only discount flows starting from time 1.
Sir, in the question why don’t we apply the same logic when we are calculating the present value of the 1.5m? Shouldn’t the discount factor be 1+time 4 discount factor since the first payment is immediately, however in the answer they use the time 5 discount factor
Annuity factors are only for annuities i.e. an equal cash flow each year.
When discount individual flows we just use the normal present value factor, so for a flow in 5 years time we multiply by the 5 year present value factor for 5 years.
It seems that you are confused about the use of discount factors and so do watch my. free Paper MA lectures on investment appraisal, because the discounting in Paper FM is not different from the discounting in Paper MA.
Okay sir. Would this logic apply to perpetuities as well if the first cashflow is immediate?
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