Throughput Accounting Question

Dear Mr. Moffat,

Please note below situation:

One of the products manufactured by a company is Product X, which sells for $40 per unit and has a material cost of $10 per unit and a direct labour cost of $7 per unit. The total direct labour budget for the year is 50,000 hours of labour time at a cost of $12 per hour. Factory overheads are $2,920,000 per year.

The company is considering the introduction of a system of throughput accounting. It has identified that machine time as the bottleneck in production. Product X needs 0.01 hours of machine time per unit produced. The maximum capacity for machine time is 4,000 hours per year.

The throughput accounting ratio is 3.41
Up to this point is very clear:

Calculate the Throughput
1) Throughput = Sales Rev – Mat Cost

Sales Cost
40 10
Throughput = 30

2) Total Factory Cost
Factory cost (all cost except materials)
3,520,000 (50,000 x 12 + 2,920,000)

3) Return per factory hour:
= Throughput / Time on key resource
Time on key resource = 0.01
Answer = 3,000

4) Cost per factory hour
= Total factory cost / total time available on key resource
Total time available on key resource = 4,000
Answer = 880

5) Throughput accounting ratio
= Return per factory hour / cost per factory hour
TA Ratio = 3.41

However, another question asks the following:

ABC Company uses throughput accounting. Machine time is the current binding constraint on production output, and management are looking for ways to increase the throughput accounting (TA) ratio for a product that the machine is used to manufacture.

Which of the following will have NO effect on the TA ratio?
A Increasing the selling price of the product
B Obtaining a lower purchase price for materials for the product
C Reducing factory costs
D Reducing the machine time per unit to make the product

The answer book gives ‘D’ as answer with the following information: Reducing the machine time per unit will increase throughput per hour and factory cost per hour by the same proportion, leaving the TA ratio unchanged.

However, if we would change in our example above the machine time per unit (let us say from 0.01hour per unit to 0.008hour per unit) clearly the TA ratio will increase as the return per factory hour would increase (to 3,750 if we use 0.008hour per unit).

I don’t see how this would impact labour hours cost and overhead costs, thus factory cost at all?

Could you please give some insight? Even if it would increase factory cost per hour it would clearly be only affecting factory cost (total machine time available would still be the same, namely 4,000 as in the example above). So I’m looking why it would effect the factory cost with the same proportion…