Question

1. You enter in a BES scheme (Individual Annuity Insurance or Private Pension System). You agree to pay 200 TL per month. You expect a return of 1% per month.
   1. What will be your expected fund size at the end of year 5?
   2. At the end of the 1^st year you find out that your investments are worth 2,480 TL. What was the rate of return on your first year?
   3. At the end of year 3 your investments are worth 8,200 TL. What is now your rate of return? What was the rate of return between year 1 and year 3?

2. You are required to evaluate and finance a big PPP (Public Private Participation) infrastructure Project.

In this type of project the bidder makes all the initial investment. In return it has the right to operate the facility for a definite period. At the end of this period turns it over to the state for free. In some cases the state can provide a guaranteed minimum income to support the entrepreneur. Nowadays most of the infrastructure projects are realized this way. The bidder has to bid the number of years it wants to operate the facility. The lowest bidder (lowest number of years of operating) usually is accorded the contract.

You are expected to base your calculations on 2 different scenarios:

      1-the state guaranteed cashflows (guaranteed)

      2-your technical team's projections (expected)

The projected cashflows of both alternatives for the first 5 years is given below. After 5 years (6th year and onwards) the cashflows will increase at the rate of 10% per year, which is the expected inflation rate.

Your company’s Minimum acceptable rate of return is 12%.

1. What is the breakeven number of years for this project for both alternatives? (the number of years required for the PV of this project =0) (round up your result to the nearest integer year).
2. If you bid for 25 years of operations what will be your NPV/IRR for both alternatives?

Year	Guaranteed Cashflow	Expected Cashflow
0	-10,000	-10,000
1	-20,000	-20,000
2	1,000	1,000
3	2,000	2,500
4	3,000	4,000
5	4,000	5,000
6	4,400	5,500	10% increase from previous period. Periods 9 and onward same 10% increase
7	4,840	6,050
8	5,324	6,655

                           

Answer 1

You have asked two unrelated questions in the same post. Further each question has multiple sub parts. I have therefore addressed all the sub parts of the first question. Please post the balance question along with all its sub parts separately.

What will be your expected fund size at the end of year 5?

FV = A / r x [(1 + r)ⁿ - 1] = 200 / 1% x [(1 + 1%)^{12 x 5} - 1] = 99,916 TL

At the end of the 1st year you find out that your investments are worth 2,480 TL. What was the rate of return on your first year?

Rate for the first year = RATE (Nper, PMT, PV, FV) = RATE (1 x 12, -200, 0, 2480) = 0.59% per month. Hence, rate of return on first year = 0.59% x 12 = 7.13%

At the end of year 3 your investments are worth 8,200 TL. What is now your rate of return? What was the rate of return between year 1 and year 3?

Rate per month = RATE (Nper, PMT, PV, FV) = RATE (3 x 12, -200, 0, 8200) = 0.73% per month. Hence, annualized rate of return = 0.73% x 12 = 8.75% per annum

Rate of return per month between year 1 and 3 = RATE (Nper, PMT, PV, FV) = RATE (2 x 12, -200, -2480, 8200) = 0.75% per month. Hence, annualized rate of return = 0.75% x 12 = 8.96% per annum