Question

You are asked to answer all the questions in the proposed case. This task assesses the following learning outcomes:

• Assess the present value of future cash flows and the future value of regular savings, annually and periodically.

• Understand the Perpetuity and annuity valuation and their factors – annual and periodical – and with various starting dates with and without

  growth.

• Demonstrate an ability to apply the technical skills in a practical context.

  LAUNCH: WEEK 10 / DELIVERY: MAY 10Tth, 2020, 23:59HRS ON MOODLE
  Submission file format: Word document with all the answers, clearly identifying all steps, results, and including comments besides each answer. Task (100 points)

  The Andreotti family—comprising Mr. Andreotti, aged 40, Mrs. Andreotti, aged 38, and their three young children— relocated to Barcelona in 2020 when Mr. Andreotti received a job offer from a leading investment banking giant. For the next six years, they rented a three-bedroom condominium for 2.000€ in Barcelona per month, which included parking and condominium fees.

  While renting made life easy, the Andreotti family began weighing the pros and cons of purchasing a flat, in the same building, that became available in June 2020. In the past three years, the real estate market had softened somewhat, and the cost of the flats were stable. The idea of home ownership as a form of pension investment appealed to the couple. The monthly rents could be used for mortgage payments instead.

  While searching for the right property they found a nice apartment with 200 square meters, very close to Diagonal-Numancia, one of the best locations of the city.

  The apartment was owned and been promoted by a state-owned construction company and was offering to type of alternatives:

Option A: renting the apartment with a perpetual contract, meaning for ever and ever. The Andreotti family thought that could be a good solution for them.

The family was very happy living in that area, and they had the chance to live there forever at an offered price of 1.600€ per month. The contract contained a clause stating that the rent price will be growing at a 0.1% monthly.

At the same time, they were not forced to ask for a loan, which represented a heavy weight in Mr. Andreotti ́s shoulders.

Option B: consisted in acquiring the property with a mortgage scheme for 40 years. The ownership was demanding an initial down payment of 1.000.000€. The total price of the apartment was still not clear, it seems there was some space for negotiation.

Mr. Andreotti new that the interest applicable rates were very attractive, around 2.4% compounded monthly, this is supposed to be the market rate for this type of activities.

Mr. Andreotti is fixing the maximum amount he can pay monthly in 2.000€.

1. 1) What is the maximum amount that Mr. Andreotti should pay? Show the calculations and explain why. (15 points)

2. 2) What is the total amount that Mr. Andreotti will pay in total after 40 years? (15 points)

3. 3) What is the present value of the rental contract offered by the owner as option A? (15 points)

4. 4) Mr. Andreotti believes that he might be interested in selling the apartment in 40 years’ time, this is when he is planning to retire.

   If the interest rates remain at the existing level, what will be the price of the apartment in that moment? (15 points)

5. 5) Mr. Andreotti is very happy for knowing how to calculate future values and present values, because this helps him in taking this type of decisions. Having said that he wonders what the future value of the rental contract could be. Can you help him? Explain your answer and show your calculations. (10 points)

6) We are still thinking that the price of the apartment is very expensive, we believe we could convince the bank of making payments only once a year, at the end of the year. The interest rate would still be the same 2.4%, how much money have we saved with this action?

a) In the payments for each year? b) in the total amount paid for the whole period? c) what is the present value of the savings?

(15 points)

7)There is a risk according to Mr. Andreotti that the interests may rise after the first 5 years. If this is the case, and the new interest rate is 5%, just after the first 5 years, how much will then be the monthly payments for the remaining 35 years of mortgage? (Hint the total initial value of the loan is depends of the offered purchase price in point 2). Explain your answer and show your calculations. (15 points)

Rubrics

100 Points	Descriptor
40%	The student demonstrates understands the concepts and uses the right approach with the right formulas
10%	The student explains the calculations, and which is the theory behind
35%	The student applies the right numbers in the formulas
10%	The student finds the right answer
5%	The student shows an accurate presentation

Points are at the end of each question.

Answer 1

1.Present value of increasing payment to perpetuity is calculated as follows:

Initial payment

_______________________

(Discount rate - growth rate)

Initial payment = 1600

Monthly Discount rate = 2.40%/12=0.20%

Monthly increase in rent = 0.10%

Hence PV of perpetuity =1600/(0.20%-0.10%) = 1600/0.1% = 1,600,000

Less Initial payment                                                          = 1,000,000

                                                                                          _________

Maximum present value of future payments                               600,000

                                                                                          _________

Equated Monthly instalment for 600,000 at 2.4% for 40 years is 1945.72

This is the maximum amount that Andreotti should pay. This is also within his budgeted amount of 2000/p.m.

2. Total amount that Andreotti will pay after 40 years is 1945.72*480=933,943.22

3. Present value of rental contract is 1,600,000 as shown in 1 above.

4. Value of the apartment after 40 years is calculated as follows:

    Rental value per month after 40 years = 1600*(1+0.1%)^480 =

    Value of apartment would be the then present value of rental of 2585.098959 to perpetuity at a discount rate of      0.20%(2.4% p.a/12) at a monthly growth rate of 0.1% which is defined as

     Rent/(Discount rate - growth rate) = /(0.20%-0.10%) = .

5.Future value of an annuity is calculated by the following formula:

   FV=C×[(1+r)n−(1+g)n​] /(r-g)

   where

• C = cash value of the first payment
• r = interest rate
• g = growth rate
• n = number of periods

    In the current context, FV=1600*[(1+0.20)^480-(1+0.10)^480]/(0.20-0.10)

   =

6.

a. Yearly payment for 600,[email protected]% p.a for 40 years works out to from PV table. The total of 12 months payment for 1st year totals to 23,348.58. Hence the savings in first year would be 152.38

b. Total amount payable on yearly basis = 23500.96*40 = 940038.58

    Total amount payable on monthly basis = 1945.72*480 = 933943.22.

    Hence total savings would be 940038.58 - 933943.22 = 6095.36.

c. Present value of savings is present value of 152.38 @ 2.4% p.a for 40 years which works out to 3890.50 taking present value annuity factor from tables.

7. The principal outstanding after 5 years of annual payment of 23500.96 is 552,257.89. When 5% rate of interest is applied on this amount for 35 years, the annual payment works out to 33,727.33 taking values from tables for the relevant data. Similarly calculating for monthly basis, the payment would be 2788.46.