2581-Advanced Financial Management-2425_S2

Doubts arise in this question as to which rate to use, and why the Rm has been used instead of the EAR.

Students should always take into consideration the periodicity of the cash flow stream to understand which rate should be used to discount the cash flows. In this question, the cash flows are expected to be monthly, and the APR is compounded monthly and so this is the correct rate to use. It should be divided by 12 to arrive at the monthly rate (5%/12 = 4.167%) which is the Rm.

Alternatively, even if students first convert the APR to an EAR as follows: EAR = (1+(5%/12))^12-1) = 5.116%
And then calculate the monthly Rm
Rm = (1+5.116%)^1/12 - 1 = 4.17%

They will arrive at the same Rm.

The key takeway is that whenever we have an annuity/perpetuity we must al- ways match the discount rate with the periodicity of the cash stream.
a. If you receive every year, you use the EAR
b. If you receive every month, you use the APR monthly compounding divided by 12.

Students have been asking why some Future values are discounted to the power of a few months instead of the whole year and vice versa to arrive at Present values.
For instance, in Exercise Set 2, question 12b, the future value has been calculated taking into consideration only 11 months and not 12. This is done because the question explicitly requires us to calculate the money Mr. Paulino will have on his 40th birthday if he only starts saving two months from now.

The Present value is always calculated for period N-1 (which is the last day of the previous month), hence if savings start in the end of February of Year N, we will discount it to the end of January of year N to find the present value. Following this reasoning, 12 months - 1 month of discounting gives us an 11 month period.