Right I have had a little go at understanding this question and trying to justify purchasing the new machine:

Dear Mr Brown,

I fully appreciate your concerns, however if you allow me to explain the benefits of my proposed investment I'm confident you will agree that it is the correct thing to do.

At the time I recommended the investment of £17,000 to purchase the current advanced electronic device, it was the correct thing to do as it was the best machine on the market.

I'm always looking for investments that will be of benefit to the company and provide a greater return on investment whilst at the same time ensuring the company has the latest most innovative equipment, and as outlined I have recently come across a machine that is better than the one we currently own.

I will attempt to address some of your concerns and provide a grieve summary regarding the costs & benefits associated with this purchase.

The purchase cost of the new machine is £20,000 whilst this is greater than the 3 x £5000 annual savings that will be achieved in its lifetime, we are also receiving £7000 trade in allowance for our current machine, which combined with the annual savings is greater than the purchase cost of the new machine.

I have not forgotten that the depreciation will increase from the current level of £4000 per annum to £6000 per annum for the new machine, however our savings will not be reduced due to the higher value of the new machine and the increased scarp value, the current machine is worth just £13k after year one, after year 2 the current machine will be worth just £9k whilst the machine will be worth £14k after its first year of depreciation.
After 4 years the current machine would have a scrap value of just £1k whilst the scrap value of the new machine on this date would be greater than this by £1k as the scrap value is expected to be £2k.

The scrap value of the current machine if we allow it to reach four years of age is £1k, by trading it in now we will receive £7k.

If we kept the current machine for 4 years, we would only see a 5.88% return when it is scrapped for a value of £1k, if we where to replace the current machine as proposed the scrap value is increased to £2k which is a 10% return on the purchase price of the machine.

The situation we have at present is this:
COSTS
Current machine cost - £17,000
BENEFITS
Scrap value benefit - £1000
SUMMARY
Total loss after 4 years: £16,000

If we invest as I propose, the situation would look like this:
COSTS
Current machine cost - £17,000
New machine cost - £20,000
Total costs - £37,000
BENEFITS
Trade in value of current machine - £7000
3 year saving (£5k per annum) - £15,000
New machine scrap value benefit - £2000
Total benefits - £24,000

Total loss after 4 years if we invest in the new machine is reduced to £13,000
This illustrates that the loss has been reduced by 18.75% reduced loss value of £3000

I believe that the figures illustrated above suggest that not only will the proposed investment ensure that we have the best available machine, but we will also make a saving of £3000

I trust the above information satisfies your concerns.

Regards