Question

QUESTION 1 When shopping for a new iPhone X today, you are considering buying it outright or on a 24 month plan (without data and sim plan).

Buying it outright costs $999 while on a 24 month plan, the repayments are $43/month. The opportunity cost of capital can be used as a discount rate and by purchasing the phone, you give up investing in shares which earn you 6% p.a.

Which is cheaper, buying the phone outright or the installment plan? Choose...24 month plan or Buying outright

How much do you save by choosing the cheaper option?

QUESTION 2

A $888 bill for council rates has just arrived. Reading through the payment options, you can choose to pay it upfront, or over two types of installment plans.

Plan A: $222 paid quarterly in arrears for 4 quarters

Plan B: $74 paid monthly in advance for 12 months

A discount rate of 16% p.a. applies.

Which is the cheapest option? Choose...Plan APlan BPay upfront

Which is the most expensive option? Choose...Pay UpfrontPlan APlan B

How much more would you pay if you picked the most expensive option compared to the cheapest option?

Answer 1

1: We need to compare the present values of both the options.

PV of Buying outright= 999

Option 2: Instalment plan

Using financial calculator

Input: N = 24

PMT = 43

I/Y = 6/12 = 0.5

Solve for PVas -1857.39

Hence the present value of the instalment option is much higher due to which select the outright purchase option.

2: We need to compare the present values of both the options.

Plan A: $222 paid quarterly in arrears for 4 quarters

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

=222*((1-1/(1+4%)^4)/(16%/4))

= 805.84

Plan B: $74 paid monthly in advance for 12 months

PV of annuity due = Annuity + Annuity*(1-1/(1+rate)^(number of terms-1))/rate

= 74+ 74*(1-1/(1+16%/12)^11)/ (16%/12)

=$826.47

Plan A is cheaper

Plan B is more expensive

Difference = 826.47-805.84 = 20.63