Some Discounting Problems 1. US with a Suppose you just graduated from UCR and h

Question

Some Discounting Problems 1. US with a Suppose you just graduated from UCR and have 2 offers. The first is a job offer at Jobs a fixed salary schedule which paid S45,000. You will expect to hold this position for 40 years and then retire. The second offer is acceptance to a 2 year master's program which will cost S35,000 a year. After you earn your master's degree, you expect to earn $70,000year for the following 38 years, at which point you will retire. The discount rate is 10%. All salary payments are made at the end of the year while tuition is paid at the start of the year. Compare the net present value of each option. Which should you take? 2. Suppose you bought a l0-year bond, which pays S50 at the end of each of the 10 consecutive years and, after the tenth year, additional pays you S1000. You just collected your seventh annual payment on the bond (a) Suppose that you decide to sell the bond now, assuming that the interest rate is 5% and this is expected to continue for the indefinite fiuture. How much can you expect to sell the bond for? (b) Suppose the interest rate has changed to 10%. Now how much can you expect to sell the bond for? 3. Comparing Investment Options Consider the following investment options Option 1 invest S100 now and get back S125 in one year Option 2: invest S75 now and get back S100 in two years (a) Find the internal rate of return for both options (b) If the interest rate is 5% which option would you prefer?

Explanation / Answer

Answer 1: -  

If Salary $45,000 for 40 yrs option opt then disc. rate = 10%

PVAF (10%.40yrs) = 9.779 app. (calculate using anuity table or discounted 1 to 40 yrs)

then net cash flow = 9.779 *45000 = $ 4,40,057 appx.

If Do 1st 2 yr master degree for 35000 a year then

Salary = $70,000 for 38 yrs

Then net present value for course master degree

Year pvf amount disc. cash outflow

1 0.909 35000 31,815

2 0.826 35000 28,910

net disc. cash flow = 60725

Calculation of netcash flow for salary   

Salary per month after degree = 70,000 p.m ,

PVAF (10%,38yrs) =8.044(it will be calculated from 3rd year to 40yrs (by using table or calculation from calculator)

Net Cash inflow of salary = 70,000*8.044 = 5,63,046

Less: Degree cash flow = 60,725

Net Cash flow = $5,02,321

Option b to completed master degree and then job is better option

Answer 2:

Period of Bond = 10 yrs , Now left period = 3 yrs from now already lapse 7 yrs

Interest rate = 5% Calculation of selling price for now=?

Year Interest on bond Pvf disc. amount

1 $50 0.952 $47.60

2 $50 0.907 $45.35

3 $50 0.864 $43.2

3 $1000 0.864 $864

selling price of bond = $ 1000.15

If Discounted rate is =10% then selling price

Year Interest on bond Pvf disc. amount

1 $50 0.909 $45.45

2 $50 0.826 $41.3

3 $50 0.751 $37.57

3 $1000 0.751 $751

selling price of bond = $ 875.32

Answer 3:-

invest today = $100 and get =$125 after 1 yr

PVF (x%,1yr) assume = X

Then

$100 = $125X

X= 100/125 = .8 (check the anuity table and find the interest rate 25%)

If invested today $75 and get $100 after 2 yrs then Assume dic rate = 30%

Then value after 2 yr = $75 *(pvaf,2yrs,30%) = 1.361 = $75*1.361 = $102.075

If disc. rate assume = 32 % then = 1.331*75 = 99.825

IRR = Lower Rate + Lower rate NPV/Lower rate NPV - uper rate Npv*difference in interest rate

= 30% + 102.075/ (102.075-99.825)* 2%

= 30% +(102.075/2.25)*2% = 30% + .907 % = 30.907%

Part B) if Interest rate is 5 % the

i) if invested today 100 for 1 yr then disc factor = 1/1.05 = 0.952

net present value = $125 *.952 - $100 = $119 - $100 = $19

ii) if invested today $75 for 2 yrs then disc factor = 1/(1.05)(1.05) = 0.907

Net Present Value after 2 yrs = $100* 0.907-$75 =$90.7 - $75 = $15.7

Option i is better

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