Question

1. Your firm has been working on an advanced technology. This technology will be available in the near term. The firm anticipates the first annual cash flow from the technology to be $118958, received three years from today. Subsequent annual cash flows will grow at 3.49% in perpetuity. What is the present value of the technology if the discount rate is 10.45%?

2. You are planning to save for retirement over the next 26 years. To do this, you will invest $833 per month in a stock account and $450 per month in a separate bond account. The return of the stock account is expected to be 12%, and the bond account will pay 6%. When you retire, you will combine your money into an account with an expected 9% return. How much will be in the stock account at retirement?

Answer 1

1. First annual cash flow at the end of third year CF1 = 118958

   Present value of perpetual cash flows at the end of three years PV₃ = CF1*(1+g) / k-g

where, k, discount rate = 10.45%
            g perpetual growth ate = 3.49%
PV₃ = 118958*(1+0.0349) / 0.1045 - 0.0349)
      = 123109.634 / 0.0696
      = 1768816.583

Total cash flows at the end of three years = 118958 + 1768816.583
                                                                    = 1887774.583

Present value of this cash flow at the rate of 10.45% = 1887774.583 / (1+0.1045)³
                                                                                    = 1401047.87

The Present value of the technology is $1401047.87

2. To find out the amount at the end of 26 years in the stock account, we will find the present value annuity of a regular payment of $833 per month.

PV_a = P*[ 1 - (1+r)^-n ] / r
where , P = $833, monthly payment
             r = 12%/12 = 1% since payment done monthly
             n = 26*12
                = 312

PV_a = 833*[ 1 - (1+0.01) ^-312 ] / 0.01
        = 833*[ 1 - 0.044847 ] / 0.01
        = 833* 95.51532
        = $79564.26

There will be $79564.26 in the stock account at the time of retirement