With the Repayment Mortgage, both Mortgage Interest and Principal are repaid to the First National Building Society each year. The repayments are equal each year, i.e. they are in the form of a Uniform Annual Series of repayments. A Repayment Mortgage is therefore sometimes referred to as an Annuity Mortgage.

Our Repayments on the £35,000 Mortgage loan are computed using the Uniform Series Formula (F5).

Our Gross Yearly Payments to First National are therefore £4,641.77

i.e. Our Gross Monthly Payments to First National are £386.81

In order to provide Life Cover, to pay the Mortgage loan in the event of the death of either Mortgager, First National required a Life Cover Premium Payment to Irish Life in the amount of £147.96 / year,

i.e. £12.33 / month

Our Gross Cash Flow Out is therefore £4789.73 / year,

i.e. £399.15 / month

                                                        ---------------


Remember our Mortgage Repayments to First National are £4641.77 each year, for 20 years !

Our Interest Paid for the 1st year will be

£35,000 x 0.1185  =  £4,147.50

Therefore our Principal Repaid for the 1st Year will be

£4,641.77 – £4,147.50  =  £494.27

Therefore our Principal Outstanding at the end of the 1st year will be

£35,000 – £494.27  =  £34,505.73

Therefore our Interest Paid for the 2nd Year will be

£34,505.73 x 0.1185  =  £4,088.93

Therefore our Principal Repaid for the 2nd Year will be

£4,641.77 – £4,088.93  =  £552.84

Therefore our Principal Outstanding at the end of the 2nd Year will be

£34,505.73 – £552.84  =  £33,952.89

Therefore our Interest Paid for the 3rd Year will be

£33,952.89 x 0.1185  =  £4,023.42

The entire Annuity Repayment process over the 20 year loan period is as tabulated in Columns C and D of Analysis Table 2 below. (Analysis Table 2 is also reproduced in Appendix 8/1.)

Note! It will be easier to follow the process of analysis if you print the Table below, separately.

---

 

Analysis Table 2

 

---

In May 1991, the Mortgage Interest applicable for Tax Relief was limited to 80% of the Interest Payment, up to a maximum Interest Payment of £4000 p.a. (See Columns C and E of Analysis Table 2.)

The Mortgage Interest applicable for Tax Relief was therefore limited to £3,200 (£4,000 x 0.8) where annual Interest Payments were greater than or equal to £4,000.

Our Interest applicable for Tax Relief was therefore £3,200 for the first three years. In all the subsequent years our Interest applicable for Tax Relief was limited to 80% of the Interest Paid.

e.g.

In Year 4	Interest Paid	=	£3,950.14
	Interest applicable for Tax Relief = £3,950.14 x 0.80	=	£3,160.11
Year 17	Interest Paid	=	£1,675.98
	Interest applicable for Tax Relief = £1,675.98 x 0.80	=	£1,340.78

 

In this Case the Tax Relief applicable to the Mortgagers is 29% p.a. Therefore, each year’s Tax Relief on Interest is calculated as 29% of the Interest applicable for Tax Relief for that year. (See Columns E and F of Analysis Table 2.)

e.g.

In Year 4	Interest applicable for Tax Relief	=	£3,160.11
	Tax Relief on Interest = £3,160.12 x 0.29	=	£916.43
Year 17	Interest applicable for Tax Relief	=	£1,340.78
	Tax Relief on Interest = £1,340.78 x 0.29	=	£388.83

 

Our Life Cover Premium Payment to Irish Life was equal each year at £147.96 p.a. In May 1991, the Premium amount applicable for Tax Relief was limited to 12.5% of Premiums Paid up to a Premium limit of £2000 p.a.

Our Premium applicable for Tax Relief was therefore £147.96 x 0.125 
                                                         
                                                              = £18.50 each year.

Our Tax Relief on Premium is calculated as 29% of the Premium Payment applicable for Tax Relief:

£18.50 x 0.29  =  £5.36 / year (See Column G of Analysis Table 2.)

i.e. £0.45 / month.

The Cash Flows applicable to the 20 Year Repayment Mortgage of Case 1 are as tabulated in Analysis Table 2.

The Net Cash Flow Out for each year is calculated by deducting the Tax Reliefs from the Gross Cash Flow Out, for each respective year. (See Columns B,F,G and H of Analysis Table 2.)

i.e. for each year

Net Cash Flow Out  =  Gross Cash Flow Out  less Tax Reliefs

e.g.

In Year 4	£3,867.94	=	£4,789.93 – £916.43 – £5.36
Year 17	£4,395.54	=	£4,789.93 – £388.83 – £5.36

 

---

 

We now know our Net Outlay (i.e. our Net Cash Flow Out) for each year.


Our investment is such that we will repay a £35,000 Mortgage over 20 years at an interest rate of 11.85% p.a.

The Final Value FV of this investment is therefore computed using the Single Payment Formula (F1).

FV  =  P( 1+i )n

i.e. FV  =  £35,000 (1.1185)20  =  £328,691.00

We want to compute the Equivalent Annual Cost of repaying our Mortgage Loan.

In order to evaluate the Equivalent Annual Cost, we must first compute the Internal Rate of Return on our Net Annual Outlays. This we do by applying the ‘Summation of present values’ (Σpv) process of Iteration.

(Refer to Example 5.8 in Section 5.3 for a refresh on the Mode of Analysis.)

                                                       ---------------


Let the Internal Rate of Return = x% p.a.

We want to compute the value of the Internal Rate of Return, x% p.a., such that: when we invest Σpv (the Sum of the present values of our Net Annual Outlays) at x% p.a. over 20 years, this will yield a Final Value of £328,691.00.

(Σpv) (1+y)20 =  FV  =  £328,691.00

The Iteration Process, by which the value of the Internal Rate of Return (x% p.a.) is computed, is as tabulated in Analysis Table 2. The Net Cash Flow Out for each year is shown in Column H of Analysis Table 2. The present values (pv) and their resultant Final Value (FV), from the successive trial values of the Internal Rate of Return (x% p.a.), are shown in Columns I, J, K and L of Analysis Table 2, Column L providing the solution of x%.

The Internal Rate of Return computes at 13.18% p.a.

i.e. Σpv  invested at 13.18% p.a. over 20 years yields £328,691.00

i.e. £27,630.32 (1.1318)20  =  £328,684.87

 

---

 

A corollary illustration, on the basis of ‘Summation of final values’ (Σfv ), will again clearly demonstrate the Investment Process and the accuracy of our mode of analysis.

When the Net Cash Flow Out each year is invested at 13.18% p.a. over the investment time period applicable to that Net Annual Cash Flow, the Summation of their final values (Σfv ) achieved at the end of the 20 year period will equal the Final Value (FV) of  £328,691.00.

The tabulation or this investment process is as follows:

IRR = 13.18% p.a.

 

Year No.	Net Outlay (P) See Column H of Analysis Table 2 £	Investment Time Period Applicable. n years	final value (fv) of Net Outlay. fv = P(1.1318)n £
1	3,856.37	19	40,532.44
2	3,856.37	18	35,812.37
3	3,856.37	17	31,641.96
4	3,867.94	16	28,041.08
5	3,886.95	15	24,897.42
6	3,908.22	14	22,118.45
7	3,932.01	13	19,661.68
8	3,958.61	12	17,489.56
9	3,988.37	11	15,569.05
10	4,021.66	10	13,870.82
11	4,058.89	9	12,369.00
12	4,100.53	8	11,040.72
13	4,147.11	7	9,865.82
14	4,199.20	6	8,826.42
15	4,257.47	5	7,906.79
16	4,322.65	4	7,092.98
17	4,395.54	3	6,372.67
18	4,477.08	2	5,735.01
19	4,568.28	1	5,170.38
20	4,670.28	0	4,670.28
FV = Σfv =			328,684.90
Q.E.D.

 

---

 

We now know the Internal Rate of Return (IRR) on our 20 Year Repayment Mortgage investment is 13.18% p.a.

We know that the Final Value (FV) of our investment is £328,691.00.

We can therefore compute the Equivalent Annual Cost (EAC) of our investment using the Uniform Series Formula (F4).