Question

1) A. Assume you are staring a new job tomorrow and will be paid $100,000/year with 2 paydays/month. If you invest 5% (of each paycheck) in your 401k a mutual fund that returns 9.5%/year, how much will this retirement account be worth after 50 years of work (at retirement)? Check your MAGNATUDES __________________________________

B. Use your answer above as the balance in your retirement account at retirement. How much could you withdraw each and every year from this account assuming that you can invest (the above money) at 5%/year and have zero in the account after 30 years?. _________________________________

2) Assume a stock has $5 dividend that you believe will grow at 6% for the next three years then at 4% forever. If you have a 7% Discount rate, what is the far value of the stock today???__________________________ Show the 5 step process.

Answer 1

1) A. Assuming the pay check remains constant at 100000/year upto retirement.

Retirement account after 50 years = $4,867,224.04

1) B. Value of annual withdrawal = $316,619.91

2) Fare value of stock today (t=0) = $183.24

D(0) = $5

D(1) = 5 * (1 + 6%) = $5.3

D(2) = 5.3 * (1 + 6%) = $5.618

D(3) = 5.618 * (1 + 6%) = $5.9551

D(4) = 5.9551 * (1 + 4%) = $6.1933

k(e) = cost of equity = 7%

g = long term growth rate = 4%

Using the long term growth rate, determining the long term value of 4% growth of dividends as of t=3

Value(t=3) = D(4) / (k(e) - g)

= 6.1933 / (7% - 4%)

= 6.1933 / 0.03

= $206.4428

P(0) = (D(1) / (1 + k(e))¹) + (D(2) / (1 + k(e))²) + (D(3) / (1 + k(e))³) + (Value(t=3) / (1 + k(e))³)

= 5.3 / (1 + 7%)¹ + 5.618 / (1 + 7%)² + 5.9551 / (1 + 7%)³ + 206.4428 / (1 + 7%)³​​​​​​​

= 4.9533 + 4.9070 + 4.8611 + 168.5188

= 183.24

Fare value of stock today (t=0) = $183.24