8.2 Case 1: Endowment Mortgage Analysis
With the Endowment Mortgage, the interest only on the Amount Borrowed is repaid to the First National Building Society. The £79.70 monthly Premium payments to Irish Life are invested in an Endowment Policy, these, to achieve payment of the Principal of £35,000 and, if the assumed growth rate is achieved, yield a Surplus of £12,770.
Our Interest Paid to First National to cover the loan is therefore
£35,000 x 0.1185 = £4,147.50 / year
= £345.62 / month.
Our Premium Paid to Irish Life into the Endowment Policy is £79.70 / month
= £956.40 / year.
Our Gross Cash Flow Out is therefore £5,103.90 / year.
= £425.32 / month.
Because, with an Endowment Mortgage, we are not repaying any of the Principal until the end of the loan period, our yearly interest payments will be on the full amount borrowed and will therefore be the same each year. Our Tax Relief (obviously assuming no Budget changes) will therefore also remain the same each year.
The Interest payment is £4,147.50 / year. In May 1991, the Mortgage Interest applicable for Tax Relief was limited to 80% of the interest paid, up to an interest paid ceiling of £4,000 p.a.
The interest paid ceiling of £4,000 therefore applies in this case, and the Interest applicable for Tax Relief is therefore £4,000 x 0.8
= £3,200 / year.
The Tax Relief on Interest paid is therefore
£3,200 x 0.29 = £928 / year = £77.33 / month,
the Tax Relief rate applicable in this case being 29% p.a.
The Premium Payment is £956.40 / year. In May 1991, the amount of the Premium on which Tax Relief was applicable was limited to 12.5% of the Premium Paid up to a ceiling of £2,000 p.a.
The Tax Relief on Premium paid is therefore
£956.40 x 0.125 x 0.29
= £34.67 / year = £2.89 / month.
Because our Gross Cash Flow Out is equal each year (being the sum of the Interest Paid and the Premium Paid each year), our Tax Relief will also be equal each year, and therefore the resultant Net Cash Flow Out will be equal each year.
Our Net Cash Flow Out is calculated by subtracting the Total Tax Relief from the Gross Cash Flow Out.
| Net Cash Flow Out | = | £5,103.90 – (£928 + £34.67) |
| = | £4,141.23 / year | |
| = | £345.10 / month |
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Our analysis of the Case 1 Endowment Mortgage therefore presents itself to us as follows:
For an Equal Amount Investment of £4,141.23 at the end of each year for a period of 20 years, we will repay a loan of £35,000 borrowed at an interest rate of 11.85% p.a. and we will achieve a Surplus of £12,770 at the end of that 20 year period —— ALL on the basis that the assumed growth rate will be achieved.
Note! The Monthly Interest Repayments to First National were computed by first compounding the interest charge annually and then dividing the resultant Yearly Interest Repayment by 12. The various other Monthly Outlays and Monthly Tax Reliefs were also computed by dividing the respective Yearly Outlay or Tax Relief by 12. Our analysis, on the basis of the end of year Net Outlay, is therefore wholly compatible with First National’s / Irish Life’s Mortgage Comparison Presentation format.
Note! The financially injurious consequences for the borrower / investor of the manner in which First National compounded and charged their Mortgage Interest has already been dealt with (as a separate issue) in Chapter 6: The Total Cost of Credit.
The Final Value (FV) of our Investment is computed using the Single Payment Formula (F1).
FV = P( 1+i )n + £12,770
i.e. FV = £35,000(1.1185)20 + £12,770
i.e. FV = £341,461
Because our Net Outlay is equal each year at £4,141.23 p.a., our Equivalent Annual Cost is therefore £4,141.23, i.e. our investments are already in the form of a Uniform Annual Series of payments. We can therefore use the Uniform Series Formula (F3) directly, in an iterative process, to compute the Internal Rate of Return (IRR) on our investments.
Note! Refer to Example 5.5 in Section 5.3 to refresh on the Mode of Analysis.
This iterative process is as follows:
Let the Internal Rate of Return = y% p.a.
|
Trial |
End of year |
Trial Value |
Computed value |
Computed value |
|
1 |
£4,141.23 |
13% |
80.946829 |
£335,219.44 |
|
2 |
£4,141.23 |
13.5% |
85.828556 |
£355,435.79 |
|
3 |
£4,141.23 |
13.15% |
82.379462 |
£341,152.30 |
|
4 |
£4,141.23 |
13.158% |
82.456626 |
£341,471.85 O.K. |
So, on the basis that the assumed growth rate of 10.75% p.a. is achieved, our Internal Rate of Return on the Endowment Mortgage in Case 1 is 13.158% p.a., with an Equivalent Annual Cost of £4,141.23 (i.e. £345.10 / month).
Because, for the Case 1 Endowment Mortgage, our Net Cash Flow Out (Net Outlay) was equal each year at £4,141.23, we were able to use the Uniform Series Formula (F3) directly, in an iterative process, to compute the Internal Rate of Return (IRR).
However, because the analysis of all Repayment Mortgages, and also the analysis of Endowment Mortgages sold in years when Tax Relief on Mortgage Interest was non-uniform over the Mortgage Term, requires the more complicated ‘Summation of present values’ (Σpv) process of Iteration to compute the IRR (the Net Outlays at the end of each year being different), we will show this Method of Analysis in use on the Mortgage Data of the Case 1 Endowment Mortgage also.
Note! Refer to Example 5.8 in Section 5.3 to refresh on this mode of analysis.
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The ‘Summation of present values’ process of iteration is as follows:
Let the Internal Rate of Return = y% p.a.
We want to compute the value of y% such that: when we invest Σpv, the Sum of the present values of each year’s Net Outlay (the present value of each year’s Net Outlay being computed by discounting that year’s Net Outlay to Time Zero by y % p.a.), at y % p.a. over 20 years, this will yield a Final Value of £341,461.00.
(Σpv) (1+y)20 = FV = £341,461.86
The Iteration Process, by which we compute the Internal Rate of Return, is as shown in Analysis Table 1 below. The Net Cash Flow Out for each year is shown in Column H of Analysis Table 1. The present values (pv) and their resultant Final Value (FV), from the successive trial values of the Internal Rate of Return (y% p.a.), are shown in Columns I, J, K and L of Analysis Table 1, Column L providing the solution of y%. (Analysis Table 1 is also reproduced in Appendix 8/1.)
The Internal Rate of Return computes at 13.158% p.a.
i.e. Σpv invested at 13.158% p.a. over 20 years yields £341,461.00
i.e. £28,817.05 invested at 13.158% p.a. over 20 years yields £341,471.75
i.e. £28,817.05 (1.13158)20 = £341,471.75
Giving an Equivalent Annual Cost of £4141.23, using Unifirm Series formula (F4).
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Note! It will be easier to follow the process of analysis if you print the Table below, separately.
Analysis Table 1
Note! Print the Table separately. The Table is not included when printing the Chapter.