Question

There are three numerical questions, you can answer them using either mathematical formula or financial calculator. No matter what method you use, you need to show the calculation steps (for math formula) or function buttons that you click.

1.a.) In the year-end of 2018, Mike Foods Inc. just spent $19.5 million to pay out the dividends and it disclosed the retained earnings of $279.5 million. In the year-end of 2017 the company had retained earnings of $221.8 million. Based on the given information, what was the net income of 2018 for Mike Foods Inc.?

1.b) Suppose Kim has $800 due in the future and the nominal rate is 6%, please find out its present value under following two conditions: (1) Semiannual compounding, discounted back 8 years (2) Quarterly compounding, discounted back 8 years. Why do the differences in the PVs occur?

1.c.)Jessica has just won a game organized by her community. As a reward, she needs to choose among three options: (A) She can choose to receive a lump-sum today of $55, (B) to receive 10 end-of-year payments of $9, or (C) to receive 30 end-of-year payments of $5. If we assume that she can earn 6% annually, which option should she choose?

Answer 1

1 a

Let RE stand for retained earnings and NI stand for net income.

Hence, RE₂₀₁₈ = RE₂₀₁₇ + NI₂₀₁₈ - Dividend₂₀₁₈

Hence, 279.5 = 221.8 + NI₂₀₁₈ - 19.5

Hence, NI₂₀₁₈ = 279.5 - 221.8 + 19.5 = $ 77.2 million

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1 b

FV = 800, i_nom = 6%

(1) Semiannual compounding, discounted back 8 years

i_semi-annual = i_nom / 2 = 6% / 2 = 3%

n = number of periods = 2 x 8 = 16

PV = FV / (1 + i_semi-annual)ⁿ = 800 / (1 + 3%)¹⁶ = $  498.53

(2) Quarterly compounding, discounted back 8 years.

i_q = i_nom / 4 = 6% / 4 = 1.5%

n = number of periods = 4 x 8 = 32

PV = FV / (1 + i_q)ⁿ = 800 / (1 + 1.5%)³² = $  496.79

The difference in PV occurs due to difference in frequency of compounding. For a given FV, higher the frequency of compounding in a year, lower will be the PV.

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1 c

(A) She can choose to receive a lump-sum today of $55,

PV_A = $ 55

(B) to receive 10 end-of-year payments of $9

Annuity, A = $ 9, n = 10, i = 6%

Hence, PV_B = A / i x [1 - (1 + i)^-n] = 9 / 6% x [1 - (1 + 6%)^-10] = $  66.24

(C) to receive 30 end-of-year payments of $5.

Annuity, A = $ 5, n = 30, i = 6%

Hence, PV_C = A / i x [1 - (1 + i)^-n] = 5 / 6% x [1 - (1 + 6%)^-30] = $  68.82

As PV_C > PV_B > PV_A, Jessica should choose option C